Question 55309
divide
{{{(8x^3+ 8y^3)/(4x^2-4xy+4y^2)}}}
Factor out the GCF in the numerator and denominator:
{{{(8*x^3+8*y^3)/(4*x^2+4*(-xy)+4*y^2)}}}
{{{8(x^3+y^3)/(4(x^2-xy+y^2))}}}  The formula for factoring the sum of cubes is:{{{highlight(u^3+v^3=(u+v)(u^2-uv+v^2))}}}.
{{{(4*2(x+y)(x^2-xy+y^2))/(4(x^2-xy+y^2))}}}  Cancel the things that match between the numerator and denominator:
{{{(cross(4)*2(x+y)*cross(x^2-xy+y^2))/(cross(4)*cross((x^2-xy+y^2)))}}}
{{{2(x+y)/1}}}
{{{highlight(2(x+y))}}}
That's usually all you need, but you could distribute the 2 and get 2x+2y.
Happy Calculating!!!