Question

factor the expression completely.\\(x^4y^3 + x^5y^2\\)

Explanation:

Step1: Identify the GCF

Find the greatest common factor (GCF) of the two terms \(x^{4}y^{3}\) and \(x^{5}y^{2}\). For the \(x\)-terms, the lowest power of \(x\) is \(x^{4}\). For the \(y\)-terms, the lowest power of \(y\) is \(y^{2}\). So the GCF is \(x^{4}y^{2}\).

Step2: Factor out the GCF

Factor out \(x^{4}y^{2}\) from each term:
\(x^{4}y^{3}+x^{5}y^{2}=x^{4}y^{2}(y + x)\)

Answer:

\(x^{4}y^{2}(x + y)\) (or \(x^{4}y^{2}(y + x)\))