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Chapter 6: Q. 396 (page 635)

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

49x2鈭�81y2

Short Answer

Expert verified

The Factored form of given polynomial is,

(7x+9y)(7x-9y)

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

49x2鈭�81y2

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 written as,

49x2鈭�81y2=7x2鈭�9y2

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

49x2鈭�81y2=(7x+9y)(7x-9y)

03

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get

(7x+9y)(7x-9y)=49x2鈭�81y249x2-7x脳9y+9y脳7x-81y2=49x2鈭�81y249x2鈭�81y2=49x2鈭�81y2LHS=RHS

Hence the factorization is correct.

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