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