Question

How do you factor `2x^2y^4 - 6x^5y^3 + 8x^3y`?

Answer 1

We can identify what all three elements have in common. One easy way to do that is decoupling the expression (this can easily be done mentally and/or by looking at the exponents).

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

`2x^2y(y^3-3x^3y^2+4x)`

One way to check this is remembering the property: `a^n*a^m=a^(n+m)`