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Use the distributive property to simplify the expression { 4x^{24} }. A.12 B.80 C.88 D.96

Question:

Use the distributive property to simplify the expression {eq}4x^{24} {/eq}.

A.12

B.80

C.88

D.96

Distributive property

An algebraic expression is an expression which consists of constants, variables and algebraic operations like addition, subtraction, product and division.

Algebraic expressions follow distributive law.

If there are two linear algebraic expressions as

{eq}\displaystyle f(x)\ =\ ax\ +\ b\\ \displaystyle g(x)\ =\ cx\ +\ d {/eq}

then according to the distributive property, their product can be written as

{eq}\displaystyle f(x)\ \times\ g(x)\ =\ (ax\ +\ b)\ \times\ ( cx\ +\ d)\ =\ ax\ \times\ (cx\ +\ d)\ +\ b\ \times\ (cx\ +\ d) {/eq}

Answer and Explanation:

Actually the question written, should be to simplify {eq}4\ \times\ 24 {/eq}.

Here using the distributive property,

1st Method,

{eq}4\ \times\ 24\\ =\ 4\ \times\ (20\ +\ 4)\\ =\ 4\ \times\ 20\ +\ 4\ \times\ 4\\ =\ 80\ +\ 16\\ =\ 96 {/eq}

2nd Method,

{eq}4\ \times\ 24\\ =\ 4\ \times\ (25\ -\ 1)\\ =\ 4\ \times\ 25\ -\ 4\ \times\ 1\\ =\ 100\ -\ 4\\ =\ 96 {/eq}

There can be many ways to solve this question. It depends on how you approach it to take it in an easy way to solve according to you.

So the correct option is D.


Learn more about this topic:

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How to Use the Distributive Property with Fractions

from High School Precalculus: Help and Review

Chapter 15 / Lesson 13
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