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Chapter 6: Q. 400 (page 635)

In the following exercises, factor completely using the difference of squares pattern, if possible.

x2-16x+64-y2

Short Answer

Expert verified

The Factored form of given polynomial is,

(x-y-8)(x+y-8)

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

x2-16x+64-y2

The formula used for factoring using the difference of squares pattern is,

a2-b2=(a+b)(a-b)

02

Step 2. Factorizing the polynomial 

The given polynomial can be also written as,

x2-16x+64-y2=(x)2-2路x路8+(8)2-y2

Using (a-b)2=a2-2ab+b2, we get

x2-16x+64-y2=(x-8)2-(y)2

Using a2-b2=(a+b)(a-b), we get

localid="1644739142803" x2-16x+64-y2=((x-8)-y)((x-8)+y)x2-16x+64-y2=(x-y-8)(x+y-8)

03

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get
(x-y-8)(x+y-8)=x2-16x+64-y2(x-y)(x+y)-8(x-y)-8(x+y)+64=x2-16x+64-y2x2-y2-8x+8y-8x-8y+64=x2-16x+64-y2x2-16x+64-y2=x2-16x+64-y2LHS=RHS

Hence the factorization is correct.

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