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

2 a^{2}

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2 b^{2}

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4 a^{2}

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4 b^{2}

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Solution

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

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