Factorise:

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

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Solution

$(a + b)^{2} - a^{2} + b^{2} \Rightarrow a^{2} + b^{2} + 2 a b - a^{2} + b^{2} \Rightarrow 2 b^{2} + 2 a b \Rightarrow 2 b (b + a)$

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

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(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}}}

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

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