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Chapter 6: Q. 394 (page 635)

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

6p2q2鈭�54p2

Short Answer

Expert verified

The Factored form of given polynomial is,

6p2(q+3)(q-3)

Step by step solution

01

Step 1. Given Information  

We are given a polynomial,

6p2q2鈭�54p2

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

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

02

Step 2. Factorizing the polynomial 

Factoring out greatest common factor 6p2, we get

6p2q2鈭�54p2=6p2(q2鈭�9)6p2q2鈭�54p2=6p2(q2鈭�32)

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

6p2q2鈭�54p2=6p2(q+3)(q-3)

03

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get

6p2(q+3)(q-3)=6p2q2鈭�54p26p2(q2-3q+3q-9)=6p2q2鈭�54p26p2(q2-9)=6p2q2鈭�54p26p2q2鈭�54p2=6p2q2鈭�54p2LHS=RHS

Hence the factorization is correct.

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