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)

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.

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