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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q. 459 (page 901)

In the following exercises, find the Greatest Common Factor in the expression.
$80 a^{2} + 120 a^{3}$

Short Answer

Expert verified

The Greatest Common Factor in the expression is $40 a^{2} (2 + 3 a)$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$80 a^{2} + 120 a^{3}$

02

Step 2. Find the GCF of each term.

We need to find the GCF of $80 a^{2}, 120 a^{3}$ ,

$80 a^{2} = 2 路 2 路 2 路 2 路 5 路 a 路 a 120 a^{3} = 2 路 2 路 2 路 3 路 5 路 a 路 a 路 a$

Take the common factors,

$= 2 路 2 路 2 路 5 路 a 路 a = 40 a^{2}$

Rewrite each term,

$= 40 a^{2} 路 2 + 40 a^{2} 路 3 a$

Factor the GCF,

$= 40 a^{2} (2 + 3 a)$

03

Step 3. Check the answer.

Simplify the GCF $40 a^{2} (2 + 3 a)$ ,

$= 40 a^{2} 路 2 + 40 a^{2} 路 3 a = 80 a^{2} + 120 a^{3}$

This is correct.

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