Factor 64p^3-125q^3

Math
64p3-125q3
Rewrite 64p3 as (4p)3.
(4p)3-125q3
Rewrite 125q3 as (5q)3.
(4p)3-(5q)3
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=4p and b=5q.
(4p-(5q))((4p)2+4p(5q)+(5q)2)
Simplify.
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Multiply 5 by -1.
(4p-5q)((4p)2+4p(5q)+(5q)2)
Apply the product rule to 4p.
(4p-5q)(42p2+4p(5q)+(5q)2)
Raise 4 to the power of 2.
(4p-5q)(16p2+4p(5q)+(5q)2)
Rewrite using the commutative property of multiplication.
(4p-5q)(16p2+4⋅5pq+(5q)2)
Multiply 4 by 5.
(4p-5q)(16p2+20pq+(5q)2)
Apply the product rule to 5q.
(4p-5q)(16p2+20pq+52q2)
Raise 5 to the power of 2.
(4p-5q)(16p2+20pq+25q2)
(4p-5q)(16p2+20pq+25q2)
Factor 64p^3-125q^3

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