Factor 125y^3-8z^3

Math
125y3-8z3
Rewrite 125y3 as (5y)3.
(5y)3-8z3
Rewrite 8z3 as (2z)3.
(5y)3-(2z)3
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=5y and b=2z.
(5y-(2z))((5y)2+5y(2z)+(2z)2)
Simplify.
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Multiply 2 by -1.
(5y-2z)((5y)2+5y(2z)+(2z)2)
Apply the product rule to 5y.
(5y-2z)(52y2+5y(2z)+(2z)2)
Raise 5 to the power of 2.
(5y-2z)(25y2+5y(2z)+(2z)2)
Rewrite using the commutative property of multiplication.
(5y-2z)(25y2+5⋅2yz+(2z)2)
Multiply 5 by 2.
(5y-2z)(25y2+10yz+(2z)2)
Apply the product rule to 2z.
(5y-2z)(25y2+10yz+22z2)
Raise 2 to the power of 2.
(5y-2z)(25y2+10yz+4z2)
(5y-2z)(25y2+10yz+4z2)
Factor 125y^3-8z^3

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