Chapter 7: Q. 7.132 (page 875)

Factor completely:
$7 y^{4} - 7$

Short Answer

Expert verified

The factored form is $7 (y^{2} + 1) (y + 1) (y - 1)$ .

Step by step solution

Step 1. Given Information

We are given a polynomial $7 y^{4} - 7$ ,

We have to factor the given polynomial.

Step 2. Factoring the polynomial

Factoring out GCF $7$ , we get

$7 y^{4} - 7 = 7 (y^{4} - 1) 7 y^{4} - 7 = 7 ({(y^{2})}^{2} - 1^{2})$

Using $x^{2} - y^{2} = (x + y) (x - y)$ , we get

$7 y^{4} - 7 = 7 (y^{2} + 1) (y^{2} - 1) 7 y^{4} - 7 = 7 (y^{2} + 1) (y^{2} - 1^{2})$

Again applying difference of square formula, we get

$7 y^{4} - 7 = 7 (y^{2} + 1) (y + 1) (y - 1)$

Step 3. Checking the factors

Using $x^{2} - y^{2} = (x + y) (x - y)$ , we get

role="math" localid="1647793519189" $7 (y^{2} + 1) (y + 1) (y - 1) = 7 y^{4} - 7 7 (y^{2} + 1) (y^{2} - 1) = 7 y^{4} - 7 7 (y^{4} - 1) = 7 y^{4} - 7 7 y^{4} - 7 = 7 y^{4} - 7 L H S = R H S$

Hence, the factors are correct.

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Factor completely:
$7 y^{4} - 7$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring the polynomial

Step 3. Checking the factors

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Factor completely:7y4-7

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring the polynomial

Step 3. Checking the factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Geometry

Decision Maths

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Factor completely:
$7 y^{4} - 7$