Question

How do you factor `y^2 + 2xy - 63x^2`?

Answer 1

Consider `(y+ax)(y-bx) = y^2+(a-b)y-(ab)x^2`

Comparing coefficients with our target quadratic, we are looking for `a` and `b` such that `a - b = 2` and `ab=63`.

Well `63 = 9*7` and `9-7 = 2`

Hence `y^2+2xy-63x^2 = (y+9x)(y-7x)`