Question

question 8 of 10
which of the binomials below is a factor of this expression?
9x^{2}+48xy + 64y^{2}
a. 3x + 8y
b. 3x - 16y
c. 3x+16y
d. 3x - 8y

Explanation:

Step1: Recognize perfect - square trinomial form

The given expression $9x^{2}+48xy + 64y^{2}$ is in the form of $a^{2}+2ab + b^{2}$, where $a = 3x$ and $b = 8y$ since $(3x)^{2}=9x^{2}$, $2\times(3x)\times(8y)=48xy$ and $(8y)^{2}=64y^{2}$.

Step2: Factor the perfect - square trinomial

Using the formula $a^{2}+2ab + b^{2}=(a + b)^{2}$, we have $9x^{2}+48xy + 64y^{2}=(3x + 8y)^{2}$.

Answer:

A. $3x + 8y$