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

Step 1. Given information.

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

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 $a^{2} - b^{2}$ .

Step 3. Write the product of conjugates.

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

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

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

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Write the product of conjugates.

Step 4. Verify.

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Factor:121m2-1.

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Write the product of conjugates.

Step 4. Verify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Statistics

Applied Mathematics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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