Question
Factorize:
$a^2 + 2ab + b^2 - c^2$
$a^2 + 2ab + b^2 - c^2$
✓
Answer
$a^2+2 a b+b^2-c^2$
Using the identity $(p+q)^2=p^2+q^2+2 p q$
$=(a+b)^2-c^2$
Using the identity $p^2-q^2=(p+q)(p-q)$
$=(a+b+c)(a+b-c)$
$\therefore a^2+2 a b+b^2-c^2$
$=(a+b+c)(a+b-c)$
Using the identity $(p+q)^2=p^2+q^2+2 p q$
$=(a+b)^2-c^2$
Using the identity $p^2-q^2=(p+q)(p-q)$
$=(a+b+c)(a+b-c)$
$\therefore a^2+2 a b+b^2-c^2$
$=(a+b+c)(a+b-c)$
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