Question

which expression is equivalent to $10x^{2}y + 25x^{2}$?
$5x^{2}(2y + 5)$
$5x^{2}y(5 + 20y)$
$10xy(x + 15y)$
$10x^{2}(y + 25)$

Explanation:

Step1: Identify greatest common factor

The terms are $10x^2y$ and $25x^2$. The greatest common factor (GCF) of $10$ and $25$ is $5$, and the GCF of $x^2y$ and $x^2$ is $x^2$. So the overall GCF is $5x^2$.

Step2: Factor out the GCF

Divide each term by $5x^2$:
$\frac{10x^2y}{5x^2} = 2y$, $\frac{25x^2}{5x^2} = 5$
Rewrite the expression as $5x^2(2y + 5)$

Step3: Verify the options

Compare the factored form to the given options to confirm a match.

Answer:

A. $5x^2(2y + 5)$