Question

Please solve this sum. I am not able to solve it.

Q.1 factorize this sum.
(x+y) (2x+3y) - (x+y) (x+1)

Answer 1

Task. Factorize this sum:

$(x+y)(2x+3y)-(x+y)(x+1)$

Solution. We should represent this expression as a product. Notice that $(x+y)$ is the common factor of both summands, so

$(x+y)(2x+3y)-(x+y)(x+1)$ =(x+y)\Big{(}(2x+3y)-(x+1)\Big{)}

$=(x+y)(2x+3y-x-1)$

$=(x+y)(x+3y-1).$

Answer.

$(x+y)(2x+3y)-(x+y)(x+1)=(x+y)(x+3y-1).$