Question

factor completely.
$24x^{7}y^{3}z^{2} + 9x^{3}y^{7}$

Explanation:

Step1: Find the GCF of coefficients and variables

For coefficients 24 and 9, GCF is 3. For \(x\)-terms, \(x^7\) and \(x^3\), GCF is \(x^3\). For \(y\)-terms, \(y^3\) and \(y^7\), GCF is \(y^3\). There's no common \(z\)-term in both, so GCF of the two terms is \(3x^3y^3\).

Step2: Factor out the GCF

Factor out \(3x^3y^3\) from \(24x^7y^3z^2 + 9x^3y^7\):
\(3x^3y^3(8x^4z^2 + 3y^4)\)

Answer:

\(3x^3y^3(8x^4z^2 + 3y^4)\)