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Chapter 7: Q. 7.131 (page 875)

Factor completely:

4a4-64

Short Answer

Expert verified

The factored form is 4a2+4(a+2)(a-2).

Step by step solution

01

Step 1. Given Information  

We are given a polynomial 4a4-64,

We have to factor the given polynomial.

02

Step 2. Factoring the polynomial  

Factoring out GCF 4, we get

role="math" localid="1647792211872" 4a4-64=4a4-164a4-64=4a22-42

Using x2-y2=(x+y)(x-y), we get

=4a2+4a2-4

Again applying difference of square formula, we get

=4a2+4a2-22=4a2+4(a+2)(a-2)

03

Step 3. Checking the factors  

Checking the factors using x2-y2=(x+y)(x-y), we get

4a2+4(a+2)(a-2)=4a4-644a2+4a2-4=4a4-644a4-16=4a4-644a4-64=4a4-64LHS=RHS

Hence, the factors are correct.

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