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# Algebra Factoring Question :V

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

Oct 21, 2018
edited by MATHEXPERTISE  Oct 21, 2018

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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

Oct 21, 2018
edited by ElectricPavlov  Oct 21, 2018

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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.

Oct 21, 2018
edited by Guest  Oct 21, 2018
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Note to Guest.....         A = B+1        AND    it does not say   A^2 - B^2 = 0

ElectricPavlov  Oct 21, 2018
#2
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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
edited by ElectricPavlov  Oct 21, 2018
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EP: Thank you Sir!.

Oct 21, 2018
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You're ALWAYS welcome......thanx for the feedback !

ElectricPavlov  Oct 21, 2018
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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

Oct 22, 2018