If A is one greater than B, what is A^2 - B^2, in terms of A and B?

MATHEXPERTISE Oct 21, 2018

#2**+2 **

**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

ElectricPavlov Oct 21, 2018

#1**0 **

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.**

Guest Oct 21, 2018

edited by
Guest
Oct 21, 2018

#2**+2 **

Best Answer

**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

ElectricPavlov Oct 21, 2018

#7**+2 **

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

ElectricPavlov Oct 22, 2018