Question:
Factorize each of the following algebraic expression:
a2 − 2ab + b2 − c2
Solution:
$a^{2}-2 a b+b^{2}-c^{2}$
$=\left(a^{2}-2 a b+b^{2}\right)-c^{2}$
$=\left(a^{2}-2 \times a \times b+b^{2}\right)-c^{2}$
$=(a-b)^{2}-c^{2}$
$=[(a-b)-c][(a-b)+c]$
$=(a-b-c)(a-b+c)$
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