Factorise:

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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