Question
Factorise:
$(a+2 b)^2+101(a+2 b)+100$
$(a+2 b)^2+101(a+2 b)+100$
✓
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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