SOLUTION: Please help me solve this and explain it. thank you! {{{ (x+2y)(_)=x^3+8y^3 }}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this and explain it. thank you! {{{ (x+2y)(_)=x^3+8y^3 }}}       Log On


   

Question 1007753: Please help me solve this and explain it. thank you! +%28x%2B2y%29%28_%29=x%5E3%2B8y%5E3+





Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can either do polynomial long division to find the factor,
f%28x%29=%28x%5E3%2B8y%5E3%29%2F%28x%2B2y%29
or you can recognize that this is the sum of two cubes.
a%5E3%2Bb%5E3=%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29
So then,
a=x
b=2y
Then,
f%28x%29=x%5E2-2xy%2B4y%5E2