How would you factor 8x2 - xy - 7y2 The 2 after the x and y are the squares. so its 8x squared - xy - 7y squared.?

Answer 1

You can factor this multivariate polynomial (a polynomial with several variables, here x and y), by looking at it as a univariate polynomial in either x or y.

This would give you a simple second order equation of the form ax2+bx+c, which you can solve. This will give you 2 solutions, say x1 and x2, and can then factor your polynomial to a(x-x1)(x-x2).

In our case:

a=8, b=-y and c=-7y2

and the solutions for this equation are x1=y and x2=-7/8*y

and this gives us

8x2 - xy -7y2 = 8(x-y)(x+7/8y) = (x-y)(8x+7y)