How do you factor #x^2 + 4xy - 5y^2#?
All the information you need is in the expression.
Read from right to left.
Find the factors of 5 which subtract to give 4.
The signs will be different (because of the minus), there will be more positives (because of +)
5 is a prime number - the only factors are 1 x 5 and we see 5 -1 = 4.
We need +5 and -1 to give +4
This leads to the two brackets:
so we have
We have three equations and four incognitas. Solving for
applying a feasible value for