Question

Factorise:
x² + 2xy + y² – a² + 2ab – b²

Answer 1

$$\begin{gathered} x^2+2xy+y^2-a^2+2ab-b^2 \\ =\left(x^2+2xy+y^2\right)-\left(a^2-2ab+b^2\right) \\ ={\left(x+y\right)}^2-{\left(a-b\right)}^2\left[a^2+2ab+b^2={\left(a+b\right)}^2\mathrm{and}{a}^2-2ab+b^2={\left(a-b\right)}^2\right] \\ =\left[\left(x+y\right)+\left(a-b\right)\right]\left[\left(x+y\right)-\left(a-b\right)\right]\left[a^2-b^2=\left(a+b\right)\left(a-b\right)\right] \\ =\left(x+y+a-b\right)\left(x+y-a+b\right) \end{gathered}$$