Partial factoring with four terms

Statement

Factorise: $x^3y - x^2y^2 + 2x - 2y$

Solution

Group the terms in pairs and factor out from each:

x^3y - x^2y^2 + 2x - 2y &= (x^3y - x^2y^2) + (2x - 2y) \\ &= x^2y(x-y) + 2(x-y) \\ &= \boxed{(x-y)(x^2y+2)} \end{aligned}$$

Links

Topics: Literal calculus
Concepts: Partial factoring · Factorisation
Skills: Factorising
Exercise type: Factorisation