Chapter 7: Q. 7.131 (page 875)

Factor completely:
$4 a^{4} - 64$

Short Answer

Expert verified

The factored form is $4 (a^{2} + 4) (a + 2) (a - 2)$ .

Step by step solution

Step 1. Given Information

We are given a polynomial $4 a^{4} - 64$ ,

We have to factor the given polynomial.

Step 2. Factoring the polynomial

Factoring out GCF $4$ , we get

role="math" localid="1647792211872" $4 a^{4} - 64 = 4 (a^{4} - 16) 4 a^{4} - 64 = 4 ({(a^{2})}^{2} - 4^{2})$

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

$= 4 (a^{2} + 4) (a^{2} - 4)$

Again applying difference of square formula, we get

$= 4 (a^{2} + 4) (a^{2} - 2^{2}) = 4 (a^{2} + 4) (a + 2) (a - 2)$

Step 3. Checking the factors

Checking the factors using $x^{2} - y^{2} = (x + y) (x - y)$ , we get

$4 (a^{2} + 4) (a + 2) (a - 2) = 4 a^{4} - 64 4 (a^{2} + 4) (a^{2} - 4) = 4 a^{4} - 64 4 (a^{4} - 16) = 4 a^{4} - 64 4 a^{4} - 64 = 4 a^{4} - 64 L H S = R H S$

Hence, the factors are correct.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Factor completely:
$4 a^{4} - 64$

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

Mechanics Maths

Logic and Functions

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Factor completely:4a4-64

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

Mechanics Maths

Logic and Functions

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Factor completely:
$4 a^{4} - 64$