Chapter 8.7, Problem 6LC

To determine

To identify the rule that use to factor the expression $k^2+12k+36.$

Answer to Problem 6LC

The square of binomial rule is used to factor the given expression.

Explanation of Solution

Given information:

Given expression $k^2+12k+36.$

Since $k^2+12k+36=k^2+2\left(k\right)\left(6\right)+6^2$

So we can write the first and last terms as squares and middle term as $2\times \text{first term}\times \text{last}\text{term}.$

Thus, we have ${\left(a+b\right)}^2=a^2+2ab+b^2$ .

Hence, the square of binomial rule is used to factor the given expression.