You can factor this out by thinking of the factors of 56 that have a sum of -1. 7 and 8 are factors of 56 and to get a sum of -1, 8 should be negative. 7 + -8 = -1
So [tex] y^{2} - xy - 56x^{2} [/tex] factored out is (y+7x)(y-8x)
We can check this using FOIL F = (y)(y) = [tex] y^{2} [/tex] O = (y)(-8x) = -8xy I = (7x)(y) = 7xy L = (7x)(-8x) = [tex] -56x^{2} [/tex] [tex] y^{2} - 8xy + 7xy - 56x^{2} [/tex] Combine like terms [tex] y^{2} - xy - 56x^{2} [/tex]
