Factor 64r^3-125s^3

Math
64r3-125s3
Rewrite 64r3 as (4r)3.
(4r)3-125s3
Rewrite 125s3 as (5s)3.
(4r)3-(5s)3
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=4r and b=5s.
(4r-(5s))((4r)2+4r(5s)+(5s)2)
Simplify.
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Multiply 5 by -1.
(4r-5s)((4r)2+4r(5s)+(5s)2)
Apply the product rule to 4r.
(4r-5s)(42r2+4r(5s)+(5s)2)
Raise 4 to the power of 2.
(4r-5s)(16r2+4r(5s)+(5s)2)
Rewrite using the commutative property of multiplication.
(4r-5s)(16r2+4⋅5rs+(5s)2)
Multiply 4 by 5.
(4r-5s)(16r2+20rs+(5s)2)
Apply the product rule to 5s.
(4r-5s)(16r2+20rs+52s2)
Raise 5 to the power of 2.
(4r-5s)(16r2+20rs+25s2)
(4r-5s)(16r2+20rs+25s2)
Factor 64r^3-125s^3

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