Factor 64t^6-27v^3

Math
64t6-27v3
Rewrite 64t6 as (4t2)3.
(4t2)3-27v3
Rewrite 27v3 as (3v)3.
(4t2)3-(3v)3
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=4t2 and b=3v.
(4t2-(3v))((4t2)2+4t2(3v)+(3v)2)
Simplify.
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Multiply 3 by -1.
(4t2-3v)((4t2)2+4t2(3v)+(3v)2)
Apply the product rule to 4t2.
(4t2-3v)(42(t2)2+4t2(3v)+(3v)2)
Raise 4 to the power of 2.
(4t2-3v)(16(t2)2+4t2(3v)+(3v)2)
Multiply the exponents in (t2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(4t2-3v)(16t2⋅2+4t2(3v)+(3v)2)
Multiply 2 by 2.
(4t2-3v)(16t4+4t2(3v)+(3v)2)
(4t2-3v)(16t4+4t2(3v)+(3v)2)
Rewrite using the commutative property of multiplication.
(4t2-3v)(16t4+4⋅3t2v+(3v)2)
Multiply 4 by 3.
(4t2-3v)(16t4+12t2v+(3v)2)
Apply the product rule to 3v.
(4t2-3v)(16t4+12t2v+32v2)
Raise 3 to the power of 2.
(4t2-3v)(16t4+12t2v+9v2)
(4t2-3v)(16t4+12t2v+9v2)
Factor 64t^6-27v^3

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