Question

Factorise:
1 + 2ab – (a² + b²)

Answer 1

$$\begin{gathered} 1+2ab-\left(a^2+b^2\right) \\ =1+2ab-a^2-b^2 \\ =1-a^2+2ab-b^2 \\ =1^2-\left(a^2-2ab+b^2\right) \end{gathered}$$

$$\begin{gathered} =1^2-{\left(a-b\right)}^2\left[a^2-2ab+b^2={\left(a-b\right)}^2\right] \\ =\left[1+\left(a-b\right)\right]\left[1-\left(a-b\right)\right]\left[a^2-b^2=\left(a+b\right)\left(a-b\right)\right] \\ =\left(1+a-b\right)\left(1-a+b\right) \end{gathered}$$