Let's expand the expression step by step:

Expand (a+b)(a-b+1):
(a+b)(a-b+1)
= a(a-b+1) + b(a-b+1)
= a^2 - ab + a + ab - b
= a^2 + a - b

Expand (a-b)(a+b-1):
(a-b)(a+b-1)
= a(a+b-1) - b(a+b-1)
= a^2 + ab - a - ab + b
= a^2 - a + b

Substitute back into the original expression:
(a+b)(a-b+1) - (a-b)(a+b-1)
= (a^2 + a - b) - (a^2 - a + b)
= a^2 + a - b - a^2 + a - b
= 2a - 2b

Therefore, (a+b)(a-b+1) - (a-b)(a+b-1) simplifies to 2a - 2b.