Question

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

Explanation:

Step1: Find greatest common factor

Identify the greatest common factor (GCF) of $10x^2y$ and $25x^2$. The GCF is $5x^2$.

Step2: Factor out the GCF

Divide each term by the GCF and write the factored form.
$\frac{10x^2y}{5x^2} + \frac{25x^2}{5x^2} = 2y + 5$
So the factored expression is $5x^2(2y + 5)$.

Step3: Verify other options

Check the expansion of other options to confirm they do not match the original expression:

• $10xy(x + 15y) = 10x^2y + 150xy^2$ (not equivalent)
• $5x^2y(5 + 20y) = 25x^2y + 100x^2y^2$ (not equivalent)
• $10x^2(y + 25) = 10x^2y + 250x^2$ (not equivalent)

Answer:

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