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Chapter 6: Q. 410 (page 636)

In the following exercises, factor completely

n4-81.

Short Answer

Expert verified

The factors of the given expression are (n-3)(n+3)(n2+9).

Step by step solution

01

Step 1. Given and explanation 

We have n4-81.

We can see that this forms a pattern of difference of two perfect squares.

We know that a2-b2=(a+b)(a-b).

Applying this, we will factorize the given expression.

02

Step 2. Factorizing the expression. 

We have n4-81.

This can be written as role="math" localid="1644629414096" (n2)2-(32)2.

Applying the property , we get

role="math" localid="1644629401616" a2-b2=(a+b)(a-b)(n2)2-(32)2=(n2+32)(n2-32)=(n2+9)(n+3)(n-3)

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