Chapter 0.3, Problem 18E

To determine

To evaluate: the factors of polynomial.

Answer to Problem 18E

The factor of polynomial $4a^2+12ab+9b^2$ is $\left(2a+3b\right)\left(2a+3b\right)$ .

Explanation of Solution

Given information:

Polynomial is given as $4a^2+12ab+9b^2$

Factorizing the given polynomial,

  $\begin{array}{c}4a^2+12ab+9b^2=4a^2+6ab+6ab+9b^2\\ 4a^2+6ab+6ab+9b^2=2a\left(2a+3b\right)+3b\left(2a+3b\right)\\ 2a\left(2a+3b\right)+3b\left(2a+3b\right)=\left(2a+3b\right)\left(2a+3b\right)\end{array}$

So,

After factorizing $\left(2a+3b\right)\left(2a+3b\right)$ .