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

4 b^{2}

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4 (a - b)^{2}

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4 (a + b)^{2}

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4 a^{2}

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Solution

The correct option is A $4 b^{2}$
$\Rightarrow (a + b)^{2} - 2 (a^{2} - b^{2}) + (a - b)^{2}$

$\Rightarrow (a + b)^{2} - 2 (a + b) (a - b) + (a - b)^{2}$

$Let x = (a + b), y = (a - b)$

$\Rightarrow x^{2} - 2 x y + y^{2}$

$\Rightarrow (x - y)^{2}$

$\Rightarrow Substituting the values of x and y,we get$

$\Rightarrow ((a + b) - (a - b))^{2}$

$\Rightarrow (a + b - a + b)^{2}$

$\Rightarrow (2 b)^{2}$

$\Rightarrow 4 b^{2}$

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Similar questions

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

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

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

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

If 2 $(a^{2} + b^{2})$ = ${(a + b)}^{2}$ , then ______________________ .

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

4 a b

- 4 a b

2 a^{2} + 2 b^{2}

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

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