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