Question:
Factorise:
ab2 − bc2 − ab + c2
Solution:
By suitably arranging the terms:
$a b^{2}-b c^{2}-a b+c^{2}=a b^{2}-a b-b c^{2}+c^{2}$
$=\left(a b^{2}-a b\right)-\left(b c^{2}-c^{2}\right)$
$=a b(b-1)-c^{2}(b-1)$
$=(b-1)\left(a b-c^{2}\right)$
$\therefore a b^{2}-b c^{2}-a b+c^{2}=(b-1)\left(a b-c^{2}\right)$
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