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Question
Simplify the following:
(2a + b)2 + (2a – b)2
Simplify
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Solution
Given expression: (2a + b)2 + (2a – b)2
Step-wise calculation:
1. Expand (2a + b)2:
(2a + b)2 = (2a)2 + 2 × (2a) × b + b2
(2a + b)2 = 4a2 + 4ab + b2
2. Expand (2a – b)2:
(2a – b)2 = (2a)2 – 2 × (2a) × b + b2
(2a – b)2 = 4a2 – 4ab + b2
3. Add the two results:
(4a2 + 4ab + b2) + (4a2 – 4ab + b2)
= 4a2 + 4ab + b2 + 4a2 – 4ab + b2
4. Combine like terms:
4a2 + 4a2 + 4ab – 4ab + b2 + b2 = 8a2 + 0 + 2b2
4a2 + 4a2 + 4ab – 4ab + b2 + b2 = 8a2 + 2b2
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