SOLUTION: Factor completely: 12x^3 - 3xy^2 If I am not mistaken in my own math I believe the answer is: 3x(4x-y)(x+y) Is this correct? Thank you

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Factor completely: 12x^3 - 3xy^2 If I am not mistaken in my own math I believe the answer is: 3x(4x-y)(x+y) Is this correct? Thank you      Log On


   

Question 70369: Factor completely:
12x^3 - 3xy^2
If I am not mistaken in my own math I believe the answer is:
3x(4x-y)(x+y)
Is this correct? Thank you
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely:
12x^3 - 3xy^2
3x(4x^2-y^2)
4x^2-y^2=(2x)^2-(y)^2 which is the difference of squares. The difference of squares can be factored highlight%28a%5E2-b%5E2=%28a%2Bb%29%28a-b%29%29. Your a=2x and b=y.
highlight%283x%282x%2By%29%282x-y%29%29
To check your answer multiply it back out and see if you get back to where you started from.
3x[2x(2x-y)+y(2x-y)]
3x[2x(2x)+2x(-y)+y(2x)+y(-y)]
3x[4x^2-2xy+2xy-y^2]
3x[4x^2-y^2]
12x^3-3xy^2 We're right!!!!
Happy Calculating!!!!