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(a + b)^2 Expansion and Visualisation

If a + b = ...

Question

If $a + b = 8, a - b = 4$ , then $a^{2} + b^{2}$ is equal to:

20

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40

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10

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30

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Solution

The correct option is B $40$
$∵ (a + b)^{2} + (a - b)^{2} = (a^{2} + b^{2} + 2 a b) + (a^{2} + b^{2} - 2 a b)$
$\Rightarrow 64 + 16 = 2 (a^{2} + b^{2})$
$\Rightarrow 80 = 2 (a^{2} + b^{2})$
$∴ a^{2} + b^{2} = 40$
Option B is correct.

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