Prove that: $(a + b)^{2} + (a - b)^{2} = 2 (a^{2} + b^{2})$ .

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Solution

We have,
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ......(1) and $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ .....(2).
Now adding (1) from (2) we get,
$(a + b)^{2} + (a - b)^{2} = 2 (a^{2} + b^{2})$ .

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