Factor(s) of $a^{2} - 2 a b + b^{2} - c^{2}$ is/are

a-b+c

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a-b-c

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Both 1 and 2

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None of the above

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Solution

The correct option is C
Both 1 and 2

$a^{2} - 2 a b + b^{2} - c^{2}$

$a^{2} - 2 a b + b^{2} = (a - b)^{2}$
$a^{2} - 2 a b + b^{2} - c^{2}$ = $(a - b)^{2} - c^{2}$
Using difference of squares $x^{2} - y^{2} = (x + y) (x - y)$
Taking $x = a - b a n d y = c$ ; we have
= $[(a - b) + c] [(a - b) - c]$

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Similar questions

Factor(s) of $a^{2} - 2 a b + b^{2} - c^{2}$ is/are

a^{2} - 2 a b - c^{2} + b^{2}

A factor of $a^{2} - 2 a b + b^{2} - c^{2}$ is ___________.

$a^{2} + b^{2} - c^{2} - d^{2} + 2 a b - 2 c d$ .

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

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