Simplify: ${(a + b)}^{2} - {(a - b)}^{2}$

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

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4 a b

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a^{2} - b^{2}

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

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Solution

The correct option is B $4 a b$
${(a + b)}^{2} - {(a - b)}^{2} = [(a + b) - (a - b)] \times [(a + b) + (a - b)]$
$(∵ a^{2} - b^{2} = (a - b) (a + b))$

$= [a + b - a + b] [a + b + a - b]$

$= (2 b) (2 a)$

$= 4 a b$

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Similar questions

Simplify :
${(a - b)}^{2} + 4 a b$

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The maximum value of the expression $y = 2 (a - x) (x + \sqrt{x^{2} + b^{2}})$ is

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

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

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