Question

factor the expression completely.\\(x^{3}y^{5}+x^{5}y^{5}\\)

Explanation:

Step1: Identify the GCF

Find the greatest common factor (GCF) of the two terms \(x^{3}y^{5}\) and \(x^{5}y^{5}\). For the \(x\)-terms, the lowest exponent is 3, so \(x^{3}\) is part of the GCF. For the \(y\)-terms, the lowest exponent is 5, so \(y^{5}\) is part of the GCF. Thus, the GCF is \(x^{3}y^{5}\).

Step2: Factor out the GCF

Factor out \(x^{3}y^{5}\) from each term:
\[

$$\begin{align*} x^{3}y^{5}+x^{5}y^{5}&=x^{3}y^{5}(1 + x^{2}) \end{align*}$$

\]

Answer:

\(x^{3}y^{5}(1 + x^{2})\)