Question

25-26 pre-college math semester a exam
question 3
completely factor each expression:
a. $2x^3y^5 + 8x^5y^3$

Explanation:

Step1: Find the GCF of coefficients and variables

The greatest common factor (GCF) of 2 and 8 is 2. For the \(x\)-terms, the GCF of \(x^3\) and \(x^5\) is \(x^3\). For the \(y\)-terms, the GCF of \(y^5\) and \(y^3\) is \(y^3\). So the GCF of the two terms is \(2x^3y^3\).

Step2: Factor out the GCF

Factor out \(2x^3y^3\) from \(2x^3y^5 + 8x^5y^3\):
\(2x^3y^3(y^2 + 4x^2)\)

Answer:

\(2x^3y^3(y^2 + 4x^2)\)