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Division of Polynomials

Factorize the...

Question

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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Division of Polynomials

Standard VIII Mathematics

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