Question

How do you factor `5x^3 + 40y^6`?

Answer 1

You can use a formula for a sum of cubes:
`a^3+b^3=(a+b)*(a^2-ab+b^2)`

Notice that `40y^6=5*8*y^6=5*2^3*(y^2)^3=5*(2y^2)^3`

Using the above formula for `a=x` and `b=2y^2` and factoring out constant `5`, we get:
`5x^3+40y^6 =5x^3+5(2y^2)^3=5(x+2y^2)(x^2-2xy^2+4y^4))`