Factorize the following algebraic expression:

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

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Solution

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

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

Using the formula, $(x - y)^{2} = x^{2} - 2 x y + y^{2}$

$= (a - b)^{2} - c^{2}$

Using, $x^{2} - y^{2} = (x + y) (x - y)$

$= (a - b - c) (a - b + c)$

$∴ a^{2} - 2 a b + b^{2} - c^{2} = (a - b - c) (a - b + c)$

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Similar questions

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

a^{2} + 2 a b + b^{2} - 16

a^{2}

b^{2}

c^{2}

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