Factor 125w^3+64m^3

Math
125w3+64m3
Rewrite 125w3 as (5w)3.
(5w)3+64m3
Rewrite 64m3 as (4m)3.
(5w)3+(4m)3
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2) where a=5w and b=4m.
(5w+4m)((5w)2-(5w)(4m)+(4m)2)
Simplify.
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Apply the product rule to 5w.
(5w+4m)(52w2-(5w)(4m)+(4m)2)
Raise 5 to the power of 2.
(5w+4m)(25w2-(5w)(4m)+(4m)2)
Multiply 5 by -1.
(5w+4m)(25w2-5w(4m)+(4m)2)
Rewrite using the commutative property of multiplication.
(5w+4m)(25w2-5⋅4(wm)+(4m)2)
Multiply -5 by 4.
(5w+4m)(25w2-20(wm)+(4m)2)
Remove parentheses.
(5w+4m)(25w2-20wm+(4m)2)
Apply the product rule to 4m.
(5w+4m)(25w2-20wm+42m2)
Raise 4 to the power of 2.
(5w+4m)(25w2-20wm+16m2)
(5w+4m)(25w2-20wm+16m2)
Factor 125w^3+64m^3

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