Factor 27m^12-125n^6

Math
27m12-125n6
Rewrite 27m12 as (3m4)3.
(3m4)3-125n6
Rewrite 125n6 as (5n2)3.
(3m4)3-(5n2)3
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=3m4 and b=5n2.
(3m4-(5n2))((3m4)2+3m4(5n2)+(5n2)2)
Simplify.
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Multiply 5 by -1.
(3m4-5n2)((3m4)2+3m4(5n2)+(5n2)2)
Apply the product rule to 3m4.
(3m4-5n2)(32(m4)2+3m4(5n2)+(5n2)2)
Raise 3 to the power of 2.
(3m4-5n2)(9(m4)2+3m4(5n2)+(5n2)2)
Multiply the exponents in (m4)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(3m4-5n2)(9m4⋅2+3m4(5n2)+(5n2)2)
Multiply 4 by 2.
(3m4-5n2)(9m8+3m4(5n2)+(5n2)2)
(3m4-5n2)(9m8+3m4(5n2)+(5n2)2)
Rewrite using the commutative property of multiplication.
(3m4-5n2)(9m8+3⋅5m4n2+(5n2)2)
Multiply 3 by 5.
(3m4-5n2)(9m8+15m4n2+(5n2)2)
Apply the product rule to 5n2.
(3m4-5n2)(9m8+15m4n2+52(n2)2)
Raise 5 to the power of 2.
(3m4-5n2)(9m8+15m4n2+25(n2)2)
Multiply the exponents in (n2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(3m4-5n2)(9m8+15m4n2+25n2⋅2)
Multiply 2 by 2.
(3m4-5n2)(9m8+15m4n2+25n4)
(3m4-5n2)(9m8+15m4n2+25n4)
(3m4-5n2)(9m8+15m4n2+25n4)
Factor 27m^12-125n^6

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