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Chapter 7: Q. 7.126 (page 873)

Factor completely:

9m2+42mn+49n2

Short Answer

Expert verified

The factored form is 3m+7n2.

Step by step solution

01

Step 1. Given Information 

We are given a polynomial 9m2+42mn+49n2,

We have to factor the given polynomial.

02

Step 2. Factoring the polynomial 

The given expression can be written as,

9m2+42mn+49n2=(3m)2+2(3m路7n)+(7n)2

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

9m2+42mn+49n2=3m+7n2

03

Step 3. Checking the factors 

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

3m+7n2=9m2+42mn+49n2(3m)2+2(3m路7n)+(7n)2=9m2+42mn+49n29m2+42mn+49n2=9m2+42mn+49n2LHS=RHS

Hence, the factors are correct.

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