SOLUTION: Which of the following is a factor of 64x^3-27y^6? A. 4x+3y^2 B. 4x+12xy-3y^2 C. 4x-12xy^2+9y^4 D. 16x^2+12xy^2+9y^4

Algebra ->  Exponents -> SOLUTION: Which of the following is a factor of 64x^3-27y^6? A. 4x+3y^2 B. 4x+12xy-3y^2 C. 4x-12xy^2+9y^4 D. 16x^2+12xy^2+9y^4      Log On


   

Question 1003821: Which of the following is a factor of 64x^3-27y^6?
A. 4x+3y^2
B. 4x+12xy-3y^2
C. 4x-12xy^2+9y^4
D. 16x^2+12xy^2+9y^4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


64x%5E3-27y%5E6
4%5E3x%5E3-3%5E3%28y%5E2%29%5E3
%284x%29%5E3-%283y%5E2%29%5E3----use the difference of cubes formula:
a%5E3+-b%5E3+=+%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29
in your case a=4x and b=3y%5E2; so, you have
%284x-3y%29%28%284x%29%5E2+%2B+4x%2A3y%5E2+%2B+%283y%5E2%29%5E2%29
%284x-3y%29%2816x%5E2+%2B+12xy%5E2+%2B+9y%5E4%29

answer: D. 16x%5E2%2B12xy%5E2%2B9y%5E4