Question

Simplify: $(1+a+b)(a+b+ab)-ab$

Answer 1

$(1+a+b)(a+b+ab)-ab$

an multiplying

$\Rightarrow a+b+ab+a^2+ab+a^2+ab+b^2+a{b}^2-ab$

$\Rightarrow a^2+b^2+ab[a+b](a+b)+2ab$

$=a^2+b^2+(a+b)[1+ab]+2ab$

$=(a+b{)}^2+(a+b\left)\right[1+ab]+2ab$

$=(a+b{)}^2(a+b\left)\right[1+ab\left]\right[\because a^2+2ab+b^2=(a+b{)}^2]$

$=(a+b)(a+b)[1+ab]$

$=(a+b)[a+b+ab+1]$

$=(a+b)[a+b+ab+1]$