`1) 8xy^3+x(x-y)^3`
`=x[8y^3+(x-y)^3]`
`=x[(2y)^3+(x-y)^3]`
`=x(x+y)(7y^2+x^2−4xy).`
`2)(a+b)^3+c^3`
`=(a+b+c)[(a+b)^2-(a+b)c+c^2]`
`=(a+b+c)(a^2+2ab+b^2-ac-bc+c^2)`
`=(a+b+c)(a^2+b^2+c^2+2ab-ac-bc).`
`3)x^2+(a+b)xy+aby^2`
`=x^2+axy+bxy+aby^2`
`=x(x+ay)+by(x+ay)`
`=(x+ay)(x+by).`
`4)x^2-(a+b)xy+aby^2`
`=x^2-axy-bxy+aby^2`
`=x(x-ay)-by(x-ay)`
`=(x-ay)(x-by).`
`5) x^2-(2a+b)xy+2aby^2`
`=x^2-2axy-bxy+2aby^2`
`=x(x-2ay)-by(x-2ay)`
`=(x-2ay)(x-by).`