Question

c. $3x^2y - 6xy - 3x^3y^2$

Explanation:

Step1: Identify the GCF

Find the greatest common factor (GCF) of the terms \(3x^{2}y\), \(-6xy\), and \(-3x^{3}y^{2}\). The GCF of the coefficients \(3\), \(-6\), \(-3\) is \(3\). For the variables, the lowest power of \(x\) is \(x^1\) (from \(-6xy\)) and the lowest power of \(y\) is \(y^1\) (from \(-6xy\)). So the GCF is \(3xy\).

Step2: Factor out the GCF

Divide each term by \(3xy\):

• \(\frac{3x^{2}y}{3xy}=x\)
• \(\frac{-6xy}{3xy}=-2\)
• \(\frac{-3x^{3}y^{2}}{3xy}=-x^{2}y\)

So, factoring out \(3xy\) from \(3x^{2}y - 6xy - 3x^{3}y^{2}\) gives \(3xy(x - 2 - x^{2}y)\).

Answer:

\(3xy(x - 2 - x^{2}y)\)