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Polynomials

Factorize:a-a...

Question

Factorize:
a − b − a² + b²

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Solution

$a - b - a^{2} + b^{2} = (a - b) - (a^{2} - b^{2}) = (a - b) - (a - b) (a + b) = (a - b) [1 - (a + b)] = (a - b) (1 - a - b)$

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Q. Factorize:

(a − b + c)² + (b − c + a)² + 2(a − b + c) (b − c + a)

\frac{\sqrt{a^{2} - b^{2}} + a}{\sqrt{a^{2} + b^{2}} + b} \div \frac{\sqrt{a^{2} + b^{2}} - b}{a - \sqrt{a^{2} - b^{2}}}

(a^{2} b^{2} c^{3} - a^{2} b^{2} c^{3} + a^{2} b^{2} c^{3}) \div a^{2} b^{2} c^{3}

\frac{a + \sqrt{a^{2} - b^{2}}}{a - \sqrt{a^{2} - b^{2}}} + \frac{a - \sqrt{a^{2} - b^{2}}}{a + \sqrt{a^{2} - b^{2}}}

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

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