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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q 6.55 (page 597)

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

Short Answer

Expert verified

Factors of $196 m^{2} - 25 n^{2}$ are $(14 m - 5 n) (14 m + 5 n)$ .

Step by step solution

01

Step 1. Given information.

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

02

Step 2. Find if the expression is of the form a2-b2.

Consider $a = 14 m, b = 5 n$ .

It can be seen that $196 m^{2} - 25 n^{2} = (14 m - 5 n) (14 m + 5 n)$ .

Therefore, the expression is of the form .

03

Step 3. Write the product of conjugates.

Note that .

It follows that $196 m^{2} - 25 n^{2} = {(14 m)}^{2} - {(5 n)}^{2}$ .

04

Step 4. Verify.

Multiply the factors as follows.

$\begin{array}{rcl} (14 m - 5 n) (14 m + 5 n) & = & {(14 m)}^{2} - {(5 n)}^{2} \\ = & 196 m^{2} - 25 n^{2} \end{array}$

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