Chapter 6: Q 6.54 (page 596)

Factor: $81 y^{2} - 1$ .

Short Answer

Expert verified

Factors of $81 y^{2} - 1$ are $(9 y - 1) (9 y + 1)$ .

Step by step solution

Step 1. Given information.

Given an expression $81 y^{2} - 1$ .

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

Consider $a = 9 y, b = 1$ .

It can be seen that $81 y^{2} - 1 = {(9 y)}^{2} - 1^{2}$ .

Therefore, the expression is of the form .

Step 3. Write the product of conjugates.

Note that .

It follows that $81 y^{2} - 1 = (9 y - 1) (9 y + 1)$ .

Step 4. Verify.

Multiply the factors as follows.

$\begin{array}{rcl} (9 y - 1) (9 y + 1) & = & {(9 y)}^{2} - 1 \\ = & 81 y^{2} - 1 \end{array}$

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Factor: $81 y^{2} - 1$ .

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:81y2-1.

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

Logic and Functions

Pure Maths

Mechanics Maths

Probability and Statistics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Factor: $81 y^{2} - 1$ .