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Addition and Subtraction of Algebraic Expression

The value of ...

Question

Question 32

The value of $(a + b)^{2} + (a - b)^{2}$ is
a) $2 a + 2 b$
b) $2 a - 2 b$
c) $2 a^{2} + 2 b^{2}$
a) $2 a^{2} + 2 b^{2}$

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Solution

We have,
$(a + b)^{2} + (a - b)^{2} = (a^{2} + b^{2} + 2 a b) + (a^{2} + b^{2} - 2 a b)$
$[∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b a n d (a - b)^{2} = a^{2} + b^{2} - 2 a b]$
$= (a^{2} + a^{2}) + (b^{2} + b^{2}) + (2 a b - 2 a b)$ [combining the like terms]
$= 2 a^{2} + 2 b^{2}$

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