Answers
We can expand the given expression:
(x + 4)²*(x - 2)
To get the equivalent one:
x³ + 6x² - 32
How to perform the operation?Here we want to expand the given expression, which is:
(x + 4)²*(x - 2)
First remember the rule:
(a + b)² = a² + 2ab + b²
So we can rewrite the first factor as:
(x + 4)² = x² + 2*4*x + 4²
= x² + 8x + 16
Replacing that in our expression we get:
(x² + 8x + 16)*(x - 2)
Now we can expand that to get:
x²*x + x²*(-2) + (8x)*x + 8x*(-2) + 16*x + 16*(-2)
= x³ - 2x² + 8x² - 16x + 16x - 32
= x³ + 6x² - 32
That is the expression expanded.
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Related Questions
Solve for x.
Thank you
Answers
Answer:
12
Step-by-step explanation:
The measure of each interior angle is [tex]\frac{180(8-2)}{8}=135^{\circ}[/tex].
[tex]\implies 135=9x+27 \\ \\ 15=x+3 \\ \\ x=12[/tex]
HELP ME PLEASE ASAP!! it’s for algebra 1 and you have to create an equation in standard form using the information in the picture. literally anyone help please i am begging i really need this done
Answers
Answer:
7x - y = 5
Step-by-step explanation:
(y - y1) = m(x - x1)
Here, (x1, y1) = (1, 2) and m = 7
(y - 2) = 7(x - 1)
y - 2 = 7x - 7
7x - y - 7 = - 2
7x - y = -2 + 7
7x - y = 5
Answer:The standard form of the equation of the line through the given point with the given slope through:(1, 2), slope = 7 is 7x - y = 5.
Step-by-step explanation:
Literal Equations
help asap !!
Answers
Answer:
Step-by-step explanation:
P = F/a
Pa = F
a = F/P
Answer:
a = [tex]\frac{F}{p}[/tex]
Step-by-step explanation:
P =[tex]\frac{F}{a}[/tex] multiple both sides by a
aP = [tex]\frac{F}{a}[/tex] [tex]\frac{a}{1}[/tex] On the right side of the equal sign, the a's cancel each other out
aP = F Divide both sides by P
[tex]\frac{aP}{P}[/tex] = [tex]\frac{F}{P}[/tex] The P's cancel out on the left side of the equal sign.
a = [tex]\frac{F}{P}[/tex]
2. Solve the system by substitution or elimination.
4x + y = 1
3y = -6x + 27
Answers
Answer:
(2, -7)
Step-by-step explanation:
4x + y = 1 3y= 6x + 27
y = 1 - 4x
3(1 - 4x) = 6x + 27
3 - 12x = 6x + 27
-12x = 6x + 24
-18x = 24
6/3
2
y = 1 - 4x
y = 1 - 4(2)
y = 1 - 8
y = -7
4x + y = 1
Answer:
Step-by-step explanation:
4x + y = 1
Divide 4x by 4, then do the same to the 1
4x/4 + y = 1/4
= x + y = 0.25
If you are solving for x, then the equation will look like this.
x = 0.25 - y (minus because you are moving the variable to the other side of the = sign)
If you are solving for y, then the equation will look like this.
y = 0.25 - x (minus because you are moving the variable on the other side of the = sign)
Answer solving for x = x = 0.25 - y
Answer solving for y = y = 0.25 - x
-------------------------------------------------------------------------------------------------------------
3y = -6x + 27
3y/3 = -6x + 27/3
y = -6x + 9
Bring -6x to the other side of the =.
6x + x = 9
6x/6 + y = 9/6
x + y = 1.5
Then you have to move the variable depending on which one you are going to solve for.
Answer solving for x = 1.5 - y
Answer solving for y = 1.5 - x
Hope this helps!
Emily was checking to see if f(x) and g(x) are inverses of each other. She found that f (g(x))
(gof)(x) = +1. She concluded that f(x) and g(x) are inverses.
Was she correct? Choose the BEST answer.
- O Yes, because both f(g(x)) equals x.
O Yes, because she found f(g(x)) and g(f(x)).
O No, because f(g(x)) does not equal g(f(x)).
O No, because f(g(x)) and g(f(x)) do not both equal x.
= and
Answers
f(x) and g(x) are not inverses because f(g(x)) and g(f(x)) do not both equal x.
What is an inverse in a function?The inverse function of a function f, also known as the inverse of f, is a mathematical function that reverses the action of f. f^{-1} is used to indicate whether the inverse of f exists if and only if f is a bijective function.For a function f:X—>Y, its inverse f^{-1}:Y—>X admits an explicit description,
it sends each element y∈Y to the special element x∈X
such that, f(x)=y.
Take the real-valued function of a real variable given by f(x) = 5x 7 as an illustration.F can be compared to the function that multiplies its input by 5 before taking 7 out of the outcome. To reverse this, one multiplies the input by 7 and divides the outcome by 5.Hence, f(x) and g(x) are not inverses because f(g(x)) and g(f(x)) do not both equal x.
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Factor the following expression.
5x5 - 3x² - 10x³ +6
(x2 – 2) (5x3 – [?]
Answers
Answer:
(x²-2) (5x³-3)
Step-by-step explanation:
rearrange terms
5x⁵-10x³-3x²+6
find one factor
(x²-2) (5x³-3)
if an analyst is studying the wait times at a clinic and the only list of patients available is on hard copy, which sampling technique is the easiest to use?
Answers
Sampling technique is the easiest to use here is systematic sampling.
Given :
if an analyst is studying the wait times at a clinic and the only list of patients available is on hard copy .
The sampling technique in this scenario is used is systematic sampling.
Systematic sampling :
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval.
k = N/n
where
k = systematic sampling interval
N = population size
n = sample size.
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How many ways can you answer a 5 multiple choice question test, where there are 4 choices for each question
Answers
There are 1024 ways to answer the 5 multiple choice question having 4 options
What is permutation ?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. A permutation is a term that describes the variety of possible arrangements or orders of objects.
We have 5 multiple choice questions.
And we are given four options to solve the question
Repeating is permitted (you can answer "c" on all of the questions if you want to)
So ,
We will use permutation to solve the question
[tex]n^{r}[/tex]
r is number of questions = 5
n is number of choices = 4
[tex]4^{5}[/tex] = 4×4×4×4×4 = 1024
There are 1024 ways to answer the 5 multiple choice question having 4 options
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Here is a solid prism.
7 cm
-5 cm-
11 cm-
Work out the volume of the prism.
cm
20 cm
Diagram NOT
accurately drawn
Answers
Answer:
1180 cm³
Step-by-step explanation:
You want the volume of a prism with an L-shaped base. It is 20 cm between bases. The outside dimensions of the L are 7 cm high by 11 cm wide; the inside dimensions are 3 cm high by 6 cm wide.
Volume formulaThe formula for the volume of a prism is ...
V = Bh
where B is the area of the base, and h is the distance between them. We know h, but we need to find B.
Base areaThe area of an L-shape is the area of the rectangle with the outside dimensions, less the area of the rectangle with the inside dimensions.
A = LW -lw
A = (11 cm)(7 cm) -(6 cm)(3 cm) = 77 cm² -18 cm² = 59 cm²
VolumeUsing the above formula, the volume is ...
V = (59 cm²)(20 cm) = 1180 cm³
The volume of the prism is 1180 cubic centimeters.
__
Additional comment
The dimensions of the inside of the L are found by subtracting the given width of the legs from the outside dimensions.
7 cm -4 cm = 3 cm . . . . inside height
11 cm -5 cm = 6 cm . . . . inside width
You can also find the area of the base by extending one or the other of the lines to divide it into two rectangles. Extending the vertical line makes the left rectangle 7 cm high by 5 cm wide. The right rectangle is 4 cm high by 6 cm wide. Then the area is 7·5 +4·6 = 35+24 = 59, as above.
Help mehhhhhhh please
Answers
Answer:
Jordan
Step-by-step explanation:
The composite number was 21.
21 can be divided by 3 and 7.
Answer: Jordan.
Step-by-step explanation:
Prime numbers are special numbers that have no divisors other than itself and [tex]1[/tex]. Prime numbers are observed in the lists created by the students.
Compound numbers are numbers that can be written as the product of at least two prime numbers. When we look at Jordan's list, we will see that the number [tex]21[/tex] breaks this rule. Because the number [tex]21[/tex] is the product of both prime numbers [tex]3[/tex] and [tex]7[/tex]. It is not a prime number. It is a composite number.
In circle R with m ∠ Q R S = 134 m∠QRS=134 and Q R = 6 QR=6 units find area of sector QRS. Round to the nearest hundredth.
Answers
Answer:
142.10 units²
Step-by-step explanation:
[tex] A = \dfrac{n}{360^\circ}\pi r^2 [/tex]
[tex] A = \dfrac{134^\circ}{360^\circ}\pi \times 6^2 [/tex]
[tex] A = \dfrac{134^\circ}{360^\circ}\pi \times 6^2 [/tex]
[tex] A = 142.10~units^2 [/tex]
Please answer! Thank youuu
Answers
Answer:
36%
Step-by-step explanation:
People with size 7 shoes = 5
People with size 7½ = 7
People with size 8 = 9
People with size 8½ = 3
People with size 9 = 1
To find out the total, you have to add all the people up:
5 + 7 + 9 + 3 + 1 = 25
The total amount of students = 25
Since you're trying to find the percentage of students who have a shoe size of 8, you have to look at how many people have that size:
People with size 8 = 9
To find out the percentage you do:
9/25 × 100 = 36%
Therefore 36% of students have a shoe size of 8
:)
Through a given point not contained in a given line, there exists ___ ___ line parallel to the given line. (two words)
Answers
There is ONLY ONE __ line parallel to the provided line that passes through a certain point that is not contained in the supplied line.
What do parallel lines mean?Parallel lines are any two or more lines that are in the same plane but never cross one another ( never intersect). Both have the same slope and are equally far from one another.
We have a line and a point outside the line;
from that point, we can generate many lines, but only one of those lines will be parallel to the line as it is. From a point, we can make many lines, but that point can only create one line that will be parallel to a given line.
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(-5)+8 x 2 please help
Answers
Answer:
11
Step-by-step explanation:
-5 + 8 x 2
Do multiplication first because PEMDAS -5 + 16
Then add: 11
Answer:
11
Step-by-step explanation:
8x2 = 16
-5+16 = 11
If you do a question like this always use PEMDAS. Do it in order.
P arenthesis
E exponents
M ultiplcation
D ivision
A ddition
S ubtraction
Please help me.
Prove that if a + b > 100, a, b, or both must be greater than 50
Answers
Answer:
Step-by-step explanation:
To prove this statement, we can use the contrapositive. The contrapositive of the statement "If a + b > 100, then a, b, or both must be greater than 50" is "If a and b are both less than or equal to 50, then a + b is less than or equal to 100."
To prove the contrapositive, we must show that if a and b are both less than or equal to 50, then a + b is indeed less than or equal to 100. This is easy to do, because if a and b are both less than or equal to 50, then the largest possible value for a is 50 and the largest possible value for b is 50. Therefore, the largest possible value for a + b is 50 + 50, which is equal to 100.
Since the contrapositive is true, it follows that the original statement must also be true. Therefore, we have proven that if a + b > 100, then a, b, or both must be greater than 50.
The yearly profits of a company is $25,000. The profits have been decreasing by 6% per year.
Part A: Write an exponential function that represents this scenario. Format your answer like: A(t)=a\left(1\pm r\right)^{t}A(t)=a(1±r)
t
Answers
An Exponential Function that can depict this situation is [tex]A(t) = 25000(0.94)^{t}[/tex]
What is an Exponential Function?
An exponential function is a mathematical function of the following form: [tex]f(x)=a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y=a(1-r)^{x}[/tex] wherein y is the final amount, a is the original amount, r is the decay factor, and x(or t) is the amount of time that has passed.
Given :
The initial amount is 25,000, and the rate of decay is 6%, or 0.06.
Write the exponential Decreasing function.
[tex]A(t) = a(1-r)^{t}[/tex]
Substitute 25,000 for a and 0.06 for r.
[tex]A(t)=25,000(1-0.06)^{t} = 25,000(0.94)^{t}[/tex]
Hence , the Situation can be represented by [tex]A(t) = 25000(0.94)^{t}[/tex]
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In a primary school class, the ratio
of boys to girls is 3: 4. If there are
12 girls in the class, what is the total
number of students in the class?
Answers
3/4= 75%
12 • 0.75 = 9
12 + 9 = 21
please help! giving brainliest to best answer!
give explanation if you can
Answers
The answer to the given function -1 . f(-8) -4 . g(4) is -7.
What are functions?
The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.
According to question, we see that f(-8)=-5, and g(4)=3
Now substituting in the given equation:
-1 . f(-8) -4 . g(4)
=(-1 . -5) - (4 . 3)
=5-12 = -7
Therefore the answer to -1 . f(-8) -4 . g(4) is -7
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10. Unlocked for sale The "sold" listings on a popular auction website included 20 sales of used "unlocked" phones of one popular model. Here are the sales prices. 450 415 495 300 325 430 370 400 325 400 235 330 304 415 405 449 355 425 299 355 (a) Find the percentile of the phone that sold for $330. (b) What was the sales price of the phone that was at the 75th percentile?
Answers
a) The percentile of the phone that sold for $330 is; 29%
b) The sales price at 75th percentile is; $425
How to find the percentile?In statistics, a percentile is a term that describes how a score compares to other scores from the same set.
From the given set of data showing the sales prices, let us sort them out from smallest to largest;
Sort the data values from smallest to largest:
235, 299, 300, 304, 325, 325, 330, 345, 355, 355, 370, 400, 400, 405, 415, 415, 425, 430, 449, 450, 495
It should be noted that 6 of the 21 data values are smaller than 325.
The percentile is then the number of data values that are less than the individual's data value divided by the number of data values in total, written as a percentage.
Thus;
Percentile = (Total number of data values/Number of data values that are less than the individual’s data value) × 100%
= 6/21 × 100%
≈ 0.2857 × 100%
= 28.57 % ≈ 29%
At 75th percentile, we have;
0.75 = x/21
x = 21 * 0.75
x = 15.75
Thus, the selling price of the phone at the 75th percentile is greater than 16 of the 21 phones. This phone has a selling price of at least $425
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In 1983, a pair of jeans cost $66.35. If a pair of jeans costs $118.10 today, what is the CPI? a. 152 b. 156 c. 178 d. 184 Please select the best answer from the choices provided A B C D
Answers
The value of CPI will be 178.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Now,
Since, In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Hence, The value of CPI will be;
CPI = 118.10 × 100 / 66.35
= 11810 / 66.35
= 178
Thus, The value of CPI will be 178.
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Solve the following equation for x:
3(x+5) = 1/9
8
4
-8
None of these choices are correct.
Answers
The solution to the linear equation 3(x + 5) = 1/9 is
x = -4 26/27.
The correct answer is option D; None of these choices are correct.
How to solve linear equation?3(x + 5) = 1/9
open parenthesis
3x + 15 = 1/9
Substract 15 from both sides
3x = 1/9 - 15
3x = (1-135)/ 9
3x = -134/9
divide both sides by 3
x = -134/9 ÷ 3
Multiply by the reciprocal of 3
x = -134/9 × 1/3
= -134/27
x = -4 26/27
Therefore, -4 26/27 is the solution that satisfies the equation 3(x + 5) = 1/9
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A ladder is leaning against a building so that the top of the ladder is touching the roof line. the bottom of the ladder is 7 feet from the building and the ladder is 25 feet long. how far is the roof line from the ground?
Answers
Using the Pythagorean theorem, we know that the roof of the building is 24 ft far from the ground.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
So, the Pythagorean theorem formula:
c² = a² + b²
Now, substitute the values in the formula to calculate the distance between the roofline and the ground.
c² = a² + b²
25² = a² + 7²
625 = a² + 49
a² = 625 - 49
a² = 576
a = √576
a = 24ft
Therefore, using the Pythagorean theorem, we know that the roof of the building is 24 ft far from the ground.
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Pick the most affordable gift (select the cheapest one): A) Laptop that originally cost $2399.99, has a discount of 40% and a sales tax of 8.2% B) A smart TV that originally cost $1799.99, has a discount of 10% and a sales tax of 4.5% C) A brand new Iphone that regularly costs 1699.99, has a 5% discount and a sales tax of 6.8% D) A GeForce 3090 RTX graphics card costs $2199.99, you have a coupon for $500 off. The sales tax is 7.5% A D B&C C B C&D
Answers
Option A) Buying a laptop will be most affordable among all the options as per the Selling price with Sales tax included.
What is Selling Price and Discount and Sales Tax?The selling price is the price at which a thing is sold. Typically, it is identified as SP. also known as a selling price on occasion.
Shop owners essentially mark this as a promotional item to give discounts to customers in a way that,
Discount equals Marked Price - Selling Price, and Discount Percentage is (Discount/Marked price) times 100.When a product is sold to a buyer, the government levies sales tax (abbreviated as ST). This tax will be collected by the merchant and paid to the government. As a result, it is added to the bill after being charged on the item's selling price.
Sales tax = Tax% of Bill AmountTotal Bill = Cost of the Item + Sales TaxFor Laptop,
Selling Price = (100-40)% of 2399.99
= 60% of 2399.99 = $ 1439.99
Total bill = 1439.99 + 8.2% of 1439.99
= 1439.99 + 118.08 = $ 1558.07
For Smart TV,
Selling Price = (100-10)% of 1799.99
= 90% 0f 1799.99 = $ 1619.99
Total bill = 1619.99 + 4.5% of 1619.99
= 1619.99 + 72.9 = $ 1692.89
For Iphone,
Selling Price = (100-5)% of 1699.99
= 95% 0f 1699.99 = $ 1614.99
Total bill = 1614.99 + 6.8% of 1614.99
= 1614.99 + 109.82 = $ 1724.81
For GeForce RTX 3090 Graphics Card,
Selling Price = 2199.99 - 500 = $ 1699.99
Total bill = 1699.99 + 7.5% of 1699.99
= 1699.99 + 127.5 = $ 1827.49
Total bill
Graphics Card > Iphone > Smart TV> Laptop.
Option A) Buying a laptop will be most affordable among all the options.
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Each student wrote a two-step equation. Peter wrote the equation 5x − 4 = 16, and Andres wrote the equation 20x − 16 = 64. The teacher looked at their equations and asked them to compare them. Complete the description of one way in which the equations are similar.
To get Andres' equation, you can multiply every number in Peter's equation by what?
Answers
Answer: 4
Step-by-step explanation:
This is Peter equation 5x − 4 = 16
This is Andres equation 20x − 16 = 64
To get from Andres's equation, you multiply every number in Peter's equation by 4
5x times 4 = 20x
-4 times 4 = -16
16 times 4 = 64
If you can, please give me a Brainliest; thank you!
Answer:
4
Step-by-step explanation:
So if you look closely at the equations, you will find out that Andres equation is the same as Peter but 4 times bigger
5x-4=16
20x-16=64
20x-16=64/5x-4=16
= 4
Now let's check
4(5x-4)=4(16)
Therefore, 4 is the answer.
Andres equation is 4 times as big as Peter (but it has the same result)
Please, give me the brainliest if you can
need the answer for my math homework
Answers
[tex]\cfrac{2}{3}-\cfrac{5}{12}\implies \cfrac{(4)2~~ - ~~(1)5}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{8~~ - ~~5}{12}\implies \cfrac{3}{12}\implies \cfrac{3\cdot 1}{3\cdot 4}\implies \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4}{5}+\cfrac{11}{12}\implies \cfrac{(12)4~~ + ~~(5)11}{\underset{\textit{using this LCD}}{60}}\implies \cfrac{48~~ + ~~55}{60}\implies \cfrac{103}{60}\implies 1\frac{43}{60}[/tex]
Which congruence theorem can be used to prove △abc ≅ △def? aas asa hl sas
Answers
As per the congruence theorem, we have proved that ΔABC ≅ΔDEF.
In math congruence theorem states that if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.
Here we need to prove ΔABC ≅ΔDEF by using the congruence theorem.
Here we have given that ΔABC and ΔDEF,
=> ∠B≅∠E [right angle]
So, we have obtained that
=> ∠A≅∠D
As we know that there is two angles and one non included side of ΔABC is congruent the two corresponding angles and one non- included side of ΔDEF, therefore, by AAS congruence rule.
So, based on the given fact we have identified that
=> ΔABC ≅ΔDEF
Therefore, the AAS congruence postulate defined that the triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.
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If f(x)=x^2-3x-2f(x)=x
2
−3x−2, then what is the remainder when f(x)f(x) is divided by x-7x−7?
Answers
When x²-3x-2 is divided by x-7, the remainder is 26, and the quotient is x+4.
What is polynomial?Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here
f(x)=x²-3x-2
divisor=x-7
When x²-3x-2 is divided by x-7,
The quotient is x+4.
The remainder is 26.
The remainder will be 26 when x²-3x-2 is divided by x-7 and the quotient will be x+4.
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The square root of (-5x)^3, for which values of x does this expression make sense?
Answers
Answer: Yes it does, it is -125x to the power of 3.
Step-by-step explanation:
Answer:MONKEY
Step-by-step explanation:
CAUSE I SAID DO
PLEASE HELP GIVING BRAINLIEST!!!!!!!!!!!!!!!!!!!!
Select all that apply. Which equations could you use to solve the following problem? Seventy-eight is 55% of what number? p = (0.85)78 = 78 = (0.55) w =
Answers
Answer:
x/78 = 55/100
Step-by-step explanation:
Use the Distributive Property to express 64 + 24
Answers
Using the the Distributive Property to express 64 + 24 is 88.
In mathematics, what is a distributive property?This property states that multiplying the sum of two or more addends by a number produces the same result as multiplying each addend separately by the number and then adding the products together.
When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar terms, we usually add the numbers first and then multiply by 5. 5(10 + 3) = 5(13) = 65.
In this case, 64 + 24 will be;
= 8(8 + 3)
= 88
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