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Chapter 6: Q. 398 (page 635)

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

48m4n2鈭�243n2

Short Answer

Expert verified

The Factored form of given polynomial is,

3n2(4m-9n)(4m+9n)

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

48m4n2鈭�243n2

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 3n2, we get

localid="1644736388246" 48m4n2鈭�243n2=3n216m2-81n248m4n2鈭�243n2=3n2(4m)2-(9n)2

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

48m4n2鈭�243n2=3n2(4m-9n)(4m+9n)

03

Step 3. Checking the factorization by multiplying

3n2(4m-9n)(4m+9n)=48m4n2鈭�243n23n2(16m2+36mn-36mx-81n2)=48m4n2鈭�243n23n2(16m2-81n2)=48m4n2鈭�243n248m4n2鈭�243n2=48m4n2鈭�243n2LHS=RHS

Hence the factorization is correct.

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