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Algebraic Identities

Question 33Th...

Question

Question 33

The value of $(a + b)^{2} - (a - b)^{2}$ is
a) $4 a b$
b) $- 4 a b$
c) $2 a^{2} + 2 b^{2}$
d) $2 a^{2} - 2 b^{2}$

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Solution

We have,
$(a + b)^{2} - (a - b)^{2} = a^{2} + b^{2} + 2 a b - (a^{2} + b^{2} - 2 a b) [∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b a n d (a - b)^{2} = a^{2} + b^{2} - 2 a b] = a^{2} + b^{2} + 2 a b - a^{2} - b^{2} + 2 a b = a^{2} + b^{2} - b^{2} - a^{2} + 2 a b + 2 a b = 4 a b$
[combining the like terms]

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