Question

Factories: a(a-1)-b (b-1)
full explain and please tell me why we use -1 at the end​

Answer 1

We have the identity $a^{2} -b^{2} = (a+b)(a-b)$

Now coming to the question

$a(a-1)-b(b-1)$

= $a^{2} - a-b^{2} + b$

= $(a^{2} - b^2) - (a-b)$

= $(a+b)(a-b) - 1*(a-b)$

=  $(a-b)(a+b-1)$

HOPE IT HELPS !!