Factor 125+8q^3

Math
125+8q3
Rewrite 125 as 53.
53+8q3
Rewrite 8q3 as (2q)3.
53+(2q)3
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2) where a=5 and b=2q.
(5+2q)(52-5(2q)+(2q)2)
Simplify.
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Raise 5 to the power of 2.
(5+2q)(25-5(2q)+(2q)2)
Multiply 2 by -5.
(5+2q)(25-10q+(2q)2)
Apply the product rule to 2q.
(5+2q)(25-10q+22q2)
Raise 2 to the power of 2.
(5+2q)(25-10q+4q2)
(5+2q)(25-10q+4q2)
Factor 125+8q^3

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