Question

factor the following expression.
$6u^{9}x^{4}y^{7} + 30u^{2}x^{5}$

Explanation:

Step1: Identify the GCF of coefficients and variables

For coefficients 6 and 30, GCF is 6. For \(u\) terms: \(u^9\) and \(u^2\), GCF is \(u^2\). For \(x\) terms: \(x^4\) and \(x^5\), GCF is \(x^4\). \(y\) is only in first term, so not in GCF.

Step2: Factor out the GCF

Factor out \(6u^2x^4\) from \(6u^9x^4y^7 + 30u^2x^5\):
\(6u^2x^4(u^7y^7 + 5x)\)

Answer:

\(6u^2x^4(u^7y^7 + 5x)\)