Question

factor the following expression.
$6u^{7}v^{5} - 24u^{3}v^{2}x^{6}$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 6 and 24. GCF(6,24) = 6.

Step2: Find GCF of variables for \(u\)

For \(u\), exponents are 7 and 3. GCF exponent is 3, so \(u^3\).

Step3: Find GCF of variables for \(v\)

For \(v\), exponents are 5 and 2. GCF exponent is 2, so \(v^2\).

Step4: Factor out GCF

Factor out \(6u^3v^2\) from \(6u^7v^5 - 24u^3v^2x^6\):
\(6u^3v^2(u^{7 - 3}v^{5 - 2} - 4x^6)\)
Simplify exponents: \(6u^3v^2(u^4v^3 - 4x^6)\)

Answer:

\(6u^3v^2(u^4v^3 - 4x^6)\)