Chapter 8.7, Problem 2LC

To determine

To factor the expression $9q^2+12q+4$ .

Answer to Problem 2LC

  $9q^2+12q+4={\left(3q+2\right)}^2$

Explanation of Solution

Given:

  $9q^2+12q+4$

Concept used:

  ${\left(a+b\right)}^2=a^2+2ab+b^2$

Calculation:

  $\begin{array}{l}9q^2+12q+4={\left(3q\right)}^2+12q+2^2\\ ={\left(3q\right)}^2+2\left(3q\right)\left(2\right)+2^2\\ ={\left(3q+2\right)}^2\end{array}$