Question:
Factorise:
$1+2 a b-\left(a^{2}+b^{2}\right)$
Solution:
$1+2 a b-\left(a^{2}+b^{2}\right)$
$=1+2 a b-a^{2}-b^{2}$
$=1-a^{2}+2 a b-b^{2}$
$=1^{2}-\left(a^{2}-2 a b+b^{2}\right)$
$=1^{2}-(a-b)^{2} \quad\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$
$=[1+(a-b)][1-(a-b)] \quad\left[a^{2}-b^{2}=(a+b)(a-b)\right]$
$=(1+a-b)(1-a+b)$
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