Question

Factor the expression 64m^12 - 27n^6p^9.

Which of the following is one of the factors?
A) 4m^4 - 3n^2p^3
B) (4m^4)^3 - (3n^2p^3)^2
C) 8m^6 - 9n^3p^4
D) (4m^3)^4 - (3np)^3

Answer 1

To factor the expression 64m^12 - 27n^6p^9, we can use the difference of cubes formula. One of the factors is (4m^4 - 3n^2p^3).

Step-by-step explanation:

To factor the expression 64m12 - 27n6p9, we can use the difference of cubes formula: a3 - b3 = (a - b)(a2 + ab + b2). In this case, let's consider 64m12 as a3 and 27n6p9 as b3. So, we have (4m4)3 - (3n2p3)3. Applying the formula, we get the factorization as (4m4 - 3n2p3)(16m8 + 12m4n2p3 + 9n4p6).