Question
Factorise: $(a+2 b)^2+101(a+2 b)+100$
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Answer
Given equation: $(a+2 b)^2+101(a+2 b)+100$
Let $(a+2 b)=x$ Then,
we have $x^2+101 x+100=x^2+100 x+x+100$
$=x(x+100)+1(x+100)$
$=(x+100)(x+1)=(a+2 b+100)(a+2 b+1)$
Let $(a+2 b)=x$ Then,
we have $x^2+101 x+100=x^2+100 x+x+100$
$=x(x+100)+1(x+100)$
$=(x+100)(x+1)=(a+2 b+100)(a+2 b+1)$
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