Chapter 6: Q. 410 (page 636)

In the following exercises, factor completely
$n^{4} - 81$ .

Short Answer

Expert verified

The factors of the given expression are $(n - 3) (n + 3) (n^{2} + 9)$ .

Step by step solution

Step 1. Given and explanation

We have $n^{4} - 81$ .

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

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

Applying this, we will factorize the given expression.

Step 2. Factorizing the expression.

We have $n^{4} - 81$ .

This can be written as role="math" localid="1644629414096" ${(n^{2})}^{2} - {(3^{2})}^{2}$ .

Applying the property , we get

role="math" localid="1644629401616" $a^{2} - b^{2} = (a + b) (a - b) {(n^{2})}^{2} - {(3^{2})}^{2} = (n^{2} + 3^{2}) (n^{2} - 3^{2}) = (n^{2} + 9) (n + 3) (n - 3)$

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In the following exercises, factor completely
$n^{4} - 81$ .

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Factorizing the expression.

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In the following exercises, factor completelyn4-81.

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Factorizing the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Geometry

Theoretical and Mathematical Physics

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely
$n^{4} - 81$ .