Algebra Factoring Question :V

GIVEN  : A = B+1

Then

A^2 - B^2 =   (B+1)^2  - B^2 = B^2 +2B +1 - B^2   = 2B+1

A^2 - B^2 =    2B+1

Not sure if I understand your question:

But, if (A + 1) = B, then:

Solve for A:
(A + 1)^2 - B^2 = 0

The left hand side factors into a product with two terms:
(1 + A - B) (1 + A + B) = 0

Split into two equations:
1 + A - B = 0 or 1 + A + B = 0

Subtract 1 - B from both sides:
A = B - 1 or 1 + A + B = 0

Subtract B + 1 from both sides:

A = B - 1 or A = -B - 1                           OR:                       B=+or-(A + 1)

CPhill: Please check this out. Thanks.

EP: Thank you Sir!.

A = B+1     then     A-1 = B

Then A^2 - B^2 =   A^2 - (A-1)^2

                         = A^2 - (A^2 -2A +1)

                         = A^2 - A^2 + 2A -1  = 2A-1