Question
Factorise:
$a - b - a^2 + b^2$
$a - b - a^2 + b^2$
✓
Answer
$a - b - a^2 + b^2$
$= (a - b) - (a^2 - b^2)$
$= (a - b) - (a - b)(a + b)$ $\big[\therefore\ \text{a}^2-\text{b}^2=(\text{a}-\text{b})(\text{a}+\text{b})\big]$
$= (a - b)(1 - a - b)$
$= (a - b) - (a^2 - b^2)$
$= (a - b) - (a - b)(a + b)$ $\big[\therefore\ \text{a}^2-\text{b}^2=(\text{a}-\text{b})(\text{a}+\text{b})\big]$
$= (a - b)(1 - a - b)$
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