Question
Factorize:
a2 + 2ab + b2 - c2
a2 + 2ab + b2 - c2
✓
Answer
a2 + 2ab + b2 - c2
Using the identity (p + q)2 = p2 + q2 + 2pq
= (a + b)2 - c2
Using the identity p2 - q2 = (p + q)(p - q)
= (a + b + c)(a + b - c)
$\therefore$ a2 + 2ab + b2 - c2 = (a + b + c)(a + b - c)
Using the identity (p + q)2 = p2 + q2 + 2pq
= (a + b)2 - c2
Using the identity p2 - q2 = (p + q)(p - q)
= (a + b + c)(a + b - c)
$\therefore$ a2 + 2ab + b2 - c2 = (a + b + c)(a + b - c)
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