Question

How do you factor the trinomial `x^2 +8xy-36y^2`?

Answer 1

`x^2+8x y -36 y^2=(x+(4 - 2 sqrt[13])y)(x+ (4 + 2sqrt[13])y)`

Explanation:

Proposing an expansion `x^2+8x y -36 y^2 = (x + a y)(x+b y) = x^2 + (a + b) x y + a b y^2`
equating the coefficients
`a+b=8,a b =-36`
and solving for `a,b` we get:
`a = 4 - 2 sqrt[13], b = 4 + 2sqrt[13]`