Chapter 8.7, Problem 2STP

For Exercises i -6, choose the correct letter.

What is the factored form of $9x^2+12x+4?$

F. ${(3x+2)}^2$

G. ${(3x+3)}^2$

H. ${(3x-2)}^2$

I. ${(3x-3)}^2$

To determine

To select the correct option for factored from of the expression $9x^2+12x+4$ from the four options $F.{\left(3x+2\right)}^{2}G.{\left(3x+3\right)}^{2}H.{\left(3x-2\right)}^{2}I.{\left(3x-3\right)}^2$

Answer to Problem 2STP

The factors of the given expression are $\left(3x+2\right)\left(3x+2\right)$ .

Explanation of Solution

Given information:

Given expression $9x^2+12x+4$

Given$9x^2+12x+4=\left({\left(3x\right)}^2+2\left(3x\right)\left(2\right)+2^2\right)$

As we know that $a^2+2ab+b^2={\left(a+b\right)}^2$

Put $a=3x,b=2$ , we get $\left({\left(3x\right)}^2+2\left(3x\right)\left(2\right)+2^2\right)={\left(3x+2\right)}^2$

  $=\left(3x+2\right)\left(3x+2\right)$

Hence, the factors of the given expression are $\left(3x+2\right)\left(3x+2\right)$ .