(A+B)(A-B)=(A+B)(A+B)

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Solution for (A+B)(A-B)=(A+B)(A+B) equation: 


Simplifying
(A + B)(A + -1B) = (A + B)(A + B)

Multiply (A + B) * (A + -1B)
(A(A + -1B) + B(A + -1B)) = (A + B)(A + B)
((A * A + -1B * A) + B(A + -1B)) = (A + B)(A + B)

Reorder the terms:
((-1AB + A2) + B(A + -1B)) = (A + B)(A + B)
((-1AB + A2) + B(A + -1B)) = (A + B)(A + B)
(-1AB + A2 + (A * B + -1B * B)) = (A + B)(A + B)
(-1AB + A2 + (AB + -1B2)) = (A + B)(A + B)

Reorder the terms:
(-1AB + AB + A2 + -1B2) = (A + B)(A + B)

Combine like terms: -1AB + AB = 0
(0 + A2 + -1B2) = (A + B)(A + B)
(A2 + -1B2) = (A + B)(A + B)

Multiply (A + B) * (A + B)
A2 + -1B2 = (A(A + B) + B(A + B))
A2 + -1B2 = ((A * A + B * A) + B(A + B))

Reorder the terms:
A2 + -1B2 = ((AB + A2) + B(A + B))
A2 + -1B2 = ((AB + A2) + B(A + B))
A2 + -1B2 = (AB + A2 + (A * B + B * B))
A2 + -1B2 = (AB + A2 + (AB + B2))

Reorder the terms:
A2 + -1B2 = (AB + AB + A2 + B2)

Combine like terms: AB + AB = 2AB
A2 + -1B2 = (2AB + A2 + B2)

Add '-1A2' to each side of the equation.
A2 + -1A2 + -1B2 = 2AB + A2 + -1A2 + B2

Combine like terms: A2 + -1A2 = 0
0 + -1B2 = 2AB + A2 + -1A2 + B2
-1B2 = 2AB + A2 + -1A2 + B2

Combine like terms: A2 + -1A2 = 0
-1B2 = 2AB + 0 + B2
-1B2 = 2AB + B2

Solving
-1B2 = 2AB + B2

Solving for variable 'B'.

Reorder the terms:
-2AB + -1B2 + -1B2 = 2AB + B2 + -2AB + -1B2

Combine like terms: -1B2 + -1B2 = -2B2
-2AB + -2B2 = 2AB + B2 + -2AB + -1B2

Reorder the terms:
-2AB + -2B2 = 2AB + -2AB + B2 + -1B2

Combine like terms: 2AB + -2AB = 0
-2AB + -2B2 = 0 + B2 + -1B2
-2AB + -2B2 = B2 + -1B2

Combine like terms: B2 + -1B2 = 0
-2AB + -2B2 = 0

Factor out the Greatest Common Factor (GCF), '-2B'.
-2B(A + B) = 0

Ignore the factor -2.

Subproblem 1
Set the factor 'B' equal to zero and attempt to solve:

Simplifying
B = 0

Solving
B = 0

Move all terms containing B to the left, all other terms to the right.

Simplifying
B = 0

Subproblem 2
Set the factor '(A + B)' equal to zero and attempt to solve:

Simplifying
A + B = 0

Solving
A + B = 0

Move all terms containing B to the left, all other terms to the right.

Add '-1A' to each side of the equation.
A + -1A + B = 0 + -1A

Combine like terms: A + -1A = 0
0 + B = 0 + -1A
B = 0 + -1A
Remove the zero:
B = -1A

Simplifying
B = -1A
Solution
B = {0, -1A}

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