Question

which expression is equivalent to $6x^{8}y^{2}+12x^{2}y^{2}$?
a) $6x^{2}y^{2}(2x^{6})$
b) $6x^{2}y^{2}(x^{4})$
c) $6x^{2}y^{2}(x^{6}+2)$
d) $6x^{2}y^{2}(x^{4}+2)$

Explanation:

Step1: Identify greatest common factor

The GCF of $6x^8y^2$ and $12x^2y^2$ is $6x^2y^2$.

Step2: Factor out the GCF

Divide each term by the GCF:
$\frac{6x^8y^2}{6x^2y^2} = x^6$, $\frac{12x^2y^2}{6x^2y^2} = 2$
Rewrite the expression: $6x^2y^2(x^6 + 2)$

Step3: Match with options

Compare the factored form to the given choices.

Answer:

C) $6x^2y^2(x^6 + 2)$