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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 7.97 (page 859)

Factor: $196 m^{2} - 25 n^{2}$

Short Answer

Expert verified

The factorization of the expression is $(14 m + 5 n) (14 m - 5 n)$

Step by step solution

01

Step 1. Given information

Given expression is $196 m^{2} - 25 n^{2}$

02

Step 2. Write the expression as the difference of square.

$196 m^{2} - 25 n^{2} = {(14 m)}^{2} - {(5 n)}^{2}$

03

Step 3. Use formula a2-b2=(a+b)(a-b)

${(14 m)}^{2} - {(5 n)}^{2} = (14 m + 5 n) (14 m - 5 n)$

04

Step 4. Check

$(14 m + 5 n) (14 m - 5 n) = {(14 m)}^{2} - {(5 n)}^{2} = 196 m^{2} - 25 n^{2}$

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