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Question
The value of (a + b)2 + (a – b)2 is ______.
Options
2a + 2b
2a – 2b
2a2 + 2b2
2a2 – 2b2
Solution
The value of (a + b)2 + (a – b)2 is 2a2 + 2b2.
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 + a2) + (b2 + b2) + (2ab – 2ab) ...[Combining the like terms]
= 2a2 + 2b2
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