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Chapter 6: Q 6.54 (page 596)

Factor:81y2-1.

Short Answer

Expert verified

Factors of81y2-1are9y-19y+1.

Step by step solution

01

Step 1. Given information.

Given an expression 81y2-1.

02

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

Consider a=9y,b=1.

It can be seen that 81y2-1=9y2-12.

Therefore, the expression is of the form .

03

Step 3. Write the product of conjugates.

Note that .

It follows that 81y2-1=9y-19y+1.

04

Step 4. Verify.

Multiply the factors as follows.

9y-19y+1=9y2-1=81y2-1

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