Question
Factorise: $x^2 - y^2 + 6y - 9$
✓
Answer
$x^2 - y^2 + 6y - 9$
$= x^2 - (y^2 - 6y + 9)$
$= x^2 - (y^2 - 2 \times y \times 3 + 3^2)$
$= x^2 - (y - 3)^2 \big[\therefore\ \text{a}^2-\text{b}^2=(\text{a}-\text{b})(\text{a}+\text{b})\big]$
$= [x + (y - 3)][x - (y - 3)]$
$= (x + y - 3)(x - y + 3)$
$= x^2 - (y^2 - 6y + 9)$
$= x^2 - (y^2 - 2 \times y \times 3 + 3^2)$
$= x^2 - (y - 3)^2 \big[\therefore\ \text{a}^2-\text{b}^2=(\text{a}-\text{b})(\text{a}+\text{b})\big]$
$= [x + (y - 3)][x - (y - 3)]$
$= (x + y - 3)(x - y + 3)$
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