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