ab^2(x+y)^p+a^2b(x+y)^(p+1)
=ab(x+y)^p [b+ax+ay]
x(x^2-y^2)-y(x-y)^2
=x(x+y)(x-y)-y(x-y)^2
=(x-y)[(x(x+y)-y(x-y)]
=(x-y)(x^2+xy-yx+y^2)
=(x-y)(x^2+y^2)
ab^2(x+y)^p+a^2b(x+y)^(p+1)
=ab(x+y)^p [b+ax+ay]
x(x^2-y^2)-y(x-y)^2
=x(x+y)(x-y)-y(x-y)^2
=(x-y)[(x(x+y)-y(x-y)]
=(x-y)(x^2+xy-yx+y^2)
=(x-y)(x^2+y^2)