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Algebraic Identities

Find the valu...

Question

Find the value of $(a - b) (a + b) + (b - a) (b + a)$ .

0

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a^{2} - b^{2}

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2 a^{2} - 2 b^{2}

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2 a^{2}

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Solution

The correct option is A $0$
Given, $(a - b) (a + b) + (b - a) (b + a)$ .

We know, $(x + y) (x - y) = x^{2} - y^{2}$ .

Then,
$(a - b) (a + b) + (b - a) (b + a)$
$= (a^{2} - b^{2}) + (b^{2} - a^{2})$
$= a^{2} - b^{2} + b^{2} - a^{2}$
$= 0$ .

Therefore, option $A$ is correct.

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