Question:
Factorise:
$(a+2 b)^{2}+101(a+2 b)+100$
Solution:
$(a+2 b)^{2}+101(a+2 b)+100=(a+2 b)^{2}+100(a+2 b)+1(a+2 b)+100$
$=(a+2 b)[(a+2 b)+100]+1[(a+2 b)+100]$
$=[(a+2 b)+1][(a+2 b)+100]$
$=(a+2 b+1)(a+2 b+100)$
Hence, factorisation of $(a+2 b)^{2}+101(a+2 b)+100$ is $(a+2 b+1)(a+2 b+100)$
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