Question

question
factor the expression completely.
$x^2y^3 + x^3y^2$

Explanation:

Step1: Identify GCF of terms

Find the greatest common factor (GCF) of \(x^{2}y^{3}\) and \(x^{3}y^{2}\). For \(x\)-terms: minimum exponent is \(2\) (\(x^{2}\)). For \(y\)-terms: minimum exponent is \(2\) (\(y^{2}\)). So GCF is \(x^{2}y^{2}\).

Step2: Factor out GCF

Factor out \(x^{2}y^{2}\) from each term:
\(x^{2}y^{3}+x^{3}y^{2}=x^{2}y^{2}(y + x)\) (since \(x^{2}y^{2}\cdot y=x^{2}y^{3}\) and \(x^{2}y^{2}\cdot x=x^{3}y^{2}\)).

Answer:

\(x^{2}y^{2}(x + y)\) (or \(x^{2}y^{2}(y + x)\), order of \(x\) and \(y\) in the binomial doesn't matter)