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Question
The value of (a + b)2 – (a – b)2 is ______.
Options
4ab
– 4ab
2a2 + 2b2
2a2 – 2b2
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Solution
The value of (a + b)2 – (a – b)2 is 4ab.
Explanation:
We have,
(a + b)2 – (a – b)2 = a2 + b2 + 2ab – (a2 + b2 – 2ab) ...[∵ (a + b)2 = a2 + b2 + 2ab and (a – b)2 = a2 + b2 – 2ab]
= a2 + b2 + 2ab – a2 – b2 + 2ab
= a2 – a2 + b2 – b2 + 2ab + 2ab
= 2ab + 2ab ...[Combining the like terms]
= 4ab
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