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Chapter 6: Q. 393 (page 635)

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

169n3鈭�n

Short Answer

Expert verified

The Factored form of given polynomial is,

n(13n-1)(13n+1)

Step by step solution

01

Step 1. Given Information 

We are given a polynomial,

169n3鈭�n

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 n, we get

169n3-n=n(169n2-1)

169n3-n=n(13n2-12)

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

169n3-n=n(13n-1)(13n+1)

03

Step 3. Checking the factorization by multiplying 

Multiplying the factors, we get

n(13n-1)(13n+1)=169n3-nn(169n2-13n+13n-1)=169n3-n169n3-n脳1=169n3-n169n3-n=169n3-nLHS=RHS

Hence the factorization is correct.

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