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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 7.115 (page 865)

Factor: $500 p^{3} + 4 q^{3}$

Short Answer

Expert verified

The factorization of the expression is $4 (5 p + q) (25 p^{2} - 5 p q + q^{2})$

Step by step solution

01

Step 1. Given information

Given expression is $500 p^{3} + 4 q^{3}$

02

Step 2. Find the Greatest Common Factor.

The G.C.F is $4$

$4 (125 p^{3} + q^{3})$

03

Step 3. Write the terms as a cube.

$a^{3} + b^{3} = 4 \{{(5 p)}^{3} + q^{3}\}$

04

Step 4. Use the sum of cubes pattern and simplify.

$(a + b) (a^{2} - a b + b^{2}) = 4 (5 p + q) \{{(5 p)}^{2} - 5 p 脳 q + q^{2}\} = 4 (5 p + q) (25 p^{2} - 5 p q + q^{2})$

05

Step 5. Check

$4 (5 p + q) (25 p^{2} - 5 p q + q^{2}) = 4 (125 p^{3} + 25 p^{2} q - 25 p^{2} q - 5 p q^{2} + 5 p q^{2} + q^{3}) = 4 (125 p^{3} + q^{3}) = 500 p^{3} + 4 q^{3}$

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