Question

Factor completely y^2-xy-56x^2

Answer 1

Answer: I got (y-8x)(y-7x) by factoring out the factors of 56, that have a sum of -1.

8 and 7 are factors of 56 when you multiply them and to get a sum of -1, 8 should change to negative. 7 + -8 = -1

Answer 2

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
`y^(2) - xy - 56x^(2)` factored out is (y+7x)(y-8x)

We can check this using FOIL
F = (y)(y) =
`y^(2)`
O = (y)(-8x) = -8xy
I = (7x)(y) = 7xy
L = (7x)(-8x) =
`-56x^(2)`

`y^(2) - 8xy + 7xy - 56x^(2)` Combine like terms

`y^(2) - xy - 56x^(2)`