Question

How do you factor `15x^2 y^3 + 10x^4 y^8`?

Answer 1

You can factor out the elements that are multiplying both parts of the equation. One step-by-step way of doing so is decoupling (which you could do mentally or by intuition, with time) your function

`3*color(green)(5*x*x*y*y*y)+2*color(green)(5*x*x)*x*x*color(green)(y*y*y)*y*y*y*y*y`

Now that we've found what both terms share, let's factor it out, multiplying what's left:

`5x^2y^3(3+2x^2y^5)`

In order to prove you're right, you can resort to the exponential law which states that `x^n*x^m=x^(n+m)` and distribute your factor. ;)