Prove that: ${(a + b)}^{2} - (a - b)^{2} = 4 a b$

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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 subtracting (2) from (1) we get,

$(a + b)^{2} - (a - b)^{2} = 4 a b$ .

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Similar questions

(a + b)^{2} + (a - b)^{2} = 2 (a^{2} + b^{2})

(a + b)^{2} - (a - b)^{2} = 4 a b

(a + b)^{2} = 4 a b

a = b

(2 a + b)^{2} = 4 a^{2} + b^{2} + 4 a b

{(a - b)}^{2}

4 a b

(a + b)^{2} - (a - b)^{2} = 4 a b

a = 4, b = 3

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