Question

Factories:
x(x+1)-y(y+1)​

Answer 1

`x(x + 1) - y(y + 1) \\ → {x}^(2) + x - {y}^(2) - y \\→( {x}^(2)- {y}^(2)) + (x - y) \\→ (x - y)(x + y) + (x - y) \\→ \boxed{ (x - y)(x + y + 1)}✓`

(x-y)(x+y+1) is the right answer.

Answer 2

`(x - y)(x + y + 1)`

Explanation:

`x(x + 1) - y(y + 1)`

`=> x^(2) + x - y^(2) - y`

Lets re-arrange it.

`=> x^(2) - y^(2) + x - y`

Now , lets expand x² - y².

`=> (x + y)(x - y) + (x - y)`

Taking ( x - y ) common ,

`=> (x - y)(x + y + 1)`