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Question
(a – b)2 + ______ = a2 – b2
Solution
(a – b)2 + 2ab – 2b2 = a2 – b2
Explanation:
Let (a – b)2 + x = a2 – b2
⇒ a2 + b2 – 2ab + x = a2 – b2 ...[∵ (a – b)2 = a2 + b2 – 2ab]
⇒ x = a2 – b2 – (a2 + b2 – 2ab)
= a2 – b2 – a2 – b2 + 2ab
= 2ab – 2ab2
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