Question

select the correct answer.
what is the completely factored form of this expression?
$9x^3y - 100xy$
$\circ$ $xy(3x - 10)(3x + 10)$
$\circ$ $xy(3x - 10)^2$
$\circ$ $xy(3x + 10)^2$
$\circ$ $(3x - 10y)(3x^2 + 30xy + 100)$

Explanation:

Step1: Factor out GCF

The given expression is \(9x^{3}y - 100xy\). The greatest common factor (GCF) of the two terms is \(xy\). Factoring out \(xy\), we get:
\(xy(9x^{2}-100)\)

Step2: Apply difference of squares

Notice that \(9x^{2}-100\) is a difference of squares, since \(9x^{2}=(3x)^{2}\) and \(100 = 10^{2}\). The formula for the difference of squares is \(a^{2}-b^{2}=(a - b)(a + b)\). Here, \(a = 3x\) and \(b = 10\). So, we can factor \(9x^{2}-100\) as \((3x - 10)(3x + 10)\).
Substituting this back into the expression from Step 1, we get:
\(xy(3x - 10)(3x + 10)\)

Answer:

A. \(xy(3x - 10)(3x + 10)\)