# 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.**

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from High School Precalculus: Help and Review

Chapter 15 / Lesson 13