Factor 64m^12-27n^6p^9 which of the following is one of the factors
16m^8-12m^4n^2p^3+9n^4p^6
16m^8+12m^4n^2p^3+9n^4p^9
4m^4-3n^2p^3
4m^4+3n^2p^3
The correct factor is 4m^4-3n^2p^3.
To factorize 64m^12-27n^6p^9, we must recognize it as the difference of cubes.
64m^12 = (4m^4)^3
27n^6p^9 = (3n^2p^3)^3
Therefore, we can rewrite the expression as:
(4m^4)^3 - (3n^2p^3)^3
Using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2), we can factorize the expression as:
(4m^4 - 3n^2p^3)(16m^8 + 12m^4n^2p^3 + 9n^4p^6)
Therefore, 4m^4-3n^2p^3 is one of the factors of 64m^12-27n^6p^9.