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

Factorise: ...

Question

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

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Solution

We have,

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

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

Thus,

$\Rightarrow [a - (b - c)] [a + (b - c)]$

$\Rightarrow (a - b + c) (a + b - c)$

Hence, this is the answer.

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Factorise $a^{2} - 81 (b - c)^{2}$

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

Factorise:

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

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