Question

factor an expression with multiple variables
an expression is completely factored when the algebraic expressions in the sum have no common factors.
you can factor a - 1 from each term.
choose efficient methods
how does writing the prime - factorization of each term help you factor an expression?
completely factor the expression 24p^5q^3 + 64p^3q^6.

Explanation:

Step1: Find the GCF of coefficients

The coefficients of the terms $24p^{5}q^{3}$ and $64p^{3}q^{6}$ are 24 and 64. The GCF of 24 and 64 is 8.

Step2: Find the GCF of variables

For the $p -$ terms, $p^{5}$ and $p^{3}$, the GCF is $p^{3}$. For the $q -$ terms, $q^{3}$ and $q^{6}$, the GCF is $q^{3}$. So the GCF of the two terms in the expression is $8p^{3}q^{3}$.

Step3: Factor out the GCF

$24p^{5}q^{3}+64p^{3}q^{6}=8p^{3}q^{3}(3p^{2} + 8q^{3})$

Answer:

$8p^{3}q^{3}(3p^{2}+8q^{3})$