Question

Rewrite x4y2-6x3y3 using a common factor

Answer 1

`x^4y^2-6x^3y^3 = x^3y^2(x - 6y)`

Explanation:

to pick out common factors, you have to find the highest common denominator. We start by listing units and variables:

we can divide the x^4y^2 by up to x^4 and up to y^2, cannot divide by non-variable numbers

we can divide 6x^3y^3 by up to x^3 and up to y^3, and by 6 if we needed to.

This means that for units, we're not dividing (because we can't simplify x^4y^2 dividing by a bare number.

For x, we can divide both by x^3, because we can divide both by x^3, but cannot divide 6x^3y^3 by x^4 or more.

For y, we can divide both by y^2, because we can divide both by y^2, but cannot divide x^4y^2 by x^3 or more.

We take the x^3y^2 and bring it in front of the brackets.

Disclaimer: when I say "cannot divide" I mean "cannot divide without introducing fractions or negative exponents".