`(ax+by)^2-(ay+bx)^2`
`=(ax+by+ay+bx)(ax+by-ay-bx)`
`=[a(x+y)+b(x+y)][a(x-y)-b(x-y)]`
`=(x+y)(a+b)(x-y)(a-b)`
\(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(=\left(ax-ay-bx+by\right)\left(ax+ay+bx+by\right)\)
\(=\left(x-y\right)\left(a-b\right)\left(x+y\right)\left(a+b\right)\)