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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q 6.53 (page 1069)

Factor: $121 m^{2} - 1$ .

Short Answer

Expert verified

Factors of $121 m^{2} - 1$ are $(11 m - 1) (11 m + 1)$ .

Step by step solution

01

Step 1. Given information.

Given an expression $121 m^{2} - 1$ .

02

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

Consider $a = 11 m, b = 1$ .

It can be seen that $121 m^{2} - 1 = {(11 m)}^{2} - 1^{2}$ .

Therefore, the expression is of the form $a^{2} - b^{2}$ .

03

Step 3. Write the product of conjugates.

Note that $a^{2} - b^{2} = (a - b) (a + b)$ .

It follows that $121 m^{2} - 1 = (11 m - 1) (11 m + 1)$ .

04

Step 4. Verify.

Multiply the factors as follows.

$\begin{array}{rcl} (11 m - 1) (11 m + 1) & = & {(11 m)}^{2} - 1 \\ = & 121 m^{2} - 1 \end{array}$

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