Factor 27c^6-64d^6

Math
27c6-64d6
Rewrite 27c6 as (3c2)3.
(3c2)3-64d6
Rewrite 64d6 as (4d2)3.
(3c2)3-(4d2)3
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=3c2 and b=4d2.
(3c2-(4d2))((3c2)2+3c2(4d2)+(4d2)2)
Simplify.
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Multiply 4 by -1.
(3c2-4d2)((3c2)2+3c2(4d2)+(4d2)2)
Apply the product rule to 3c2.
(3c2-4d2)(32(c2)2+3c2(4d2)+(4d2)2)
Raise 3 to the power of 2.
(3c2-4d2)(9(c2)2+3c2(4d2)+(4d2)2)
Multiply the exponents in (c2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(3c2-4d2)(9c2⋅2+3c2(4d2)+(4d2)2)
Multiply 2 by 2.
(3c2-4d2)(9c4+3c2(4d2)+(4d2)2)
(3c2-4d2)(9c4+3c2(4d2)+(4d2)2)
Rewrite using the commutative property of multiplication.
(3c2-4d2)(9c4+3⋅4c2d2+(4d2)2)
Multiply 3 by 4.
(3c2-4d2)(9c4+12c2d2+(4d2)2)
Apply the product rule to 4d2.
(3c2-4d2)(9c4+12c2d2+42(d2)2)
Raise 4 to the power of 2.
(3c2-4d2)(9c4+12c2d2+16(d2)2)
Multiply the exponents in (d2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(3c2-4d2)(9c4+12c2d2+16d2⋅2)
Multiply 2 by 2.
(3c2-4d2)(9c4+12c2d2+16d4)
(3c2-4d2)(9c4+12c2d2+16d4)
(3c2-4d2)(9c4+12c2d2+16d4)
Factor 27c^6-64d^6

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