Question

factor the following expression.
$8u^{6}v^{3}y^{9}-24u^{2}v^{4}$

Explanation:

Step1: Identify the GCF of coefficients and variables

The GCF of 8 and 24 is 8. For the \(u\)-terms, the GCF of \(u^6\) and \(u^2\) is \(u^2\). For the \(v\)-terms, the GCF of \(v^3\) and \(v^4\) is \(v^3\). The \(y\)-term only appears in the first term, so we don't include it in the GCF. So the GCF is \(8u^2v^3\).

Step2: Divide each term by the GCF

Divide \(8u^6v^3y^9\) by \(8u^2v^3\): \(\frac{8u^6v^3y^9}{8u^2v^3}=u^{6 - 2}y^9 = u^4y^9\). Divide \(-24u^2v^4\) by \(8u^2v^3\): \(\frac{-24u^2v^4}{8u^2v^3}=- 3v\).

Step3: Write the factored form

Using the distributive property (reverse of factoring out GCF), we get \(8u^2v^3(u^4y^9 - 3v)\).

Answer:

\(8u^2v^3(u^4y^9 - 3v)\)