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(a+b)(a-b) Expansion and Visualisation

Factorise: ...

Question

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

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Solution

We have,

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

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

$= a^{2} - b^{2} - a^{2} - b^{2} - 2 a b$

$= - 2 b^{2} - 2 a b$

$= - 2 b (a + b)$

Hence, this is the answer.

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