(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 + b) = (a + b)(a + -1b)

Multiply (a + b) * (a + b)
(a(a + b) + b(a + b)) = (a + b)(a + -1b)
((a * a + b * a) + b(a + b)) = (a + b)(a + -1b)

Reorder the terms:
((ab + a2) + b(a + b)) = (a + b)(a + -1b)
((ab + a2) + b(a + b)) = (a + b)(a + -1b)
(ab + a2 + (a * b + b * b)) = (a + b)(a + -1b)
(ab + a2 + (ab + b2)) = (a + b)(a + -1b)

Reorder the terms:
(ab + ab + a2 + b2) = (a + b)(a + -1b)

Combine like terms: ab + ab = 2ab
(2ab + a2 + b2) = (a + b)(a + -1b)

Multiply (a + b) * (a + -1b)
2ab + a2 + b2 = (a(a + -1b) + b(a + -1b))
2ab + a2 + b2 = ((a * a + -1b * a) + b(a + -1b))

Reorder the terms:
2ab + a2 + b2 = ((-1ab + a2) + b(a + -1b))
2ab + a2 + b2 = ((-1ab + a2) + b(a + -1b))
2ab + a2 + b2 = (-1ab + a2 + (a * b + -1b * b))
2ab + a2 + b2 = (-1ab + a2 + (ab + -1b2))

Reorder the terms:
2ab + a2 + b2 = (-1ab + ab + a2 + -1b2)

Combine like terms: -1ab + ab = 0
2ab + a2 + b2 = (0 + a2 + -1b2)
2ab + a2 + b2 = (a2 + -1b2)

Add '-1a2' to each side of the equation.
2ab + a2 + -1a2 + b2 = a2 + -1a2 + -1b2

Combine like terms: a2 + -1a2 = 0
2ab + 0 + b2 = a2 + -1a2 + -1b2
2ab + b2 = a2 + -1a2 + -1b2

Combine like terms: a2 + -1a2 = 0
2ab + b2 = 0 + -1b2
2ab + b2 = -1b2

Solving
2ab + b2 = -1b2

Solving for variable 'a'.

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

Add '-1b2' to each side of the equation.
2ab + b2 + -1b2 = -1b2 + -1b2

Combine like terms: b2 + -1b2 = 0
2ab + 0 = -1b2 + -1b2
2ab = -1b2 + -1b2

Combine like terms: -1b2 + -1b2 = -2b2
2ab = -2b2

Divide each side by '2b'.
a = -1b

Simplifying
a = -1b

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