# How do you factor # 9x^2+24xy+16y^2#?

##### 2 Answers

#### Explanation:

Note that:

#9x^2 = (3x)^2#

#24xy = 2(3x)(4y)#

#16y^2 = (4y)^2#

So:

#9x^2+24xy+16y^2 = (3x)^2+2(3x)(4y)+(4y)^2#

is in the form:

#A^2+2AB+B^2 = (A+B)^2#

So putting

#9x^2+24xy+16y^2 = (3x+4y)^2#

#### Explanation:

We are given:

We want to obtain an expression of the form:

where

Expanding this form we get:

From the expression we are given we must satisfy the following equations:

For

For

With these options, we now need to find the ones that when combined will give us the

Hence, we must choose

So the factored expression