(a+b)(x+y)=(b+a)(y+x)

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Solution for (a+b)(x+y)=(b+a)(y+x) equation: 


Simplifying
(a + b)(x + y) = (b + a)(y + x)

Multiply (a + b) * (x + y)
(a(x + y) + b(x + y)) = (b + a)(y + x)
((x * a + y * a) + b(x + y)) = (b + a)(y + x)
((ax + ay) + b(x + y)) = (b + a)(y + x)
(ax + ay + (x * b + y * b)) = (b + a)(y + x)
(ax + ay + (bx + by)) = (b + a)(y + x)
(ax + ay + bx + by) = (b + a)(y + x)

Reorder the terms:
ax + ay + bx + by = (a + b)(y + x)

Reorder the terms:
ax + ay + bx + by = (a + b)(x + y)

Multiply (a + b) * (x + y)
ax + ay + bx + by = (a(x + y) + b(x + y))
ax + ay + bx + by = ((x * a + y * a) + b(x + y))
ax + ay + bx + by = ((ax + ay) + b(x + y))
ax + ay + bx + by = (ax + ay + (x * b + y * b))
ax + ay + bx + by = (ax + ay + (bx + by))
ax + ay + bx + by = (ax + ay + bx + by)

Add '-1ax' to each side of the equation.
ax + ay + bx + -1ax + by = ax + ay + bx + -1ax + by

Reorder the terms:
ax + -1ax + ay + bx + by = ax + ay + bx + -1ax + by

Combine like terms: ax + -1ax = 0
0 + ay + bx + by = ax + ay + bx + -1ax + by
ay + bx + by = ax + ay + bx + -1ax + by

Reorder the terms:
ay + bx + by = ax + -1ax + ay + bx + by

Combine like terms: ax + -1ax = 0
ay + bx + by = 0 + ay + bx + by
ay + bx + by = ay + bx + by

Add '-1ay' to each side of the equation.
ay + bx + -1ay + by = ay + bx + -1ay + by

Reorder the terms:
ay + -1ay + bx + by = ay + bx + -1ay + by

Combine like terms: ay + -1ay = 0
0 + bx + by = ay + bx + -1ay + by
bx + by = ay + bx + -1ay + by

Reorder the terms:
bx + by = ay + -1ay + bx + by

Combine like terms: ay + -1ay = 0
bx + by = 0 + bx + by
bx + by = bx + by

Add '-1bx' to each side of the equation.
bx + -1bx + by = bx + -1bx + by

Combine like terms: bx + -1bx = 0
0 + by = bx + -1bx + by
by = bx + -1bx + by

Combine like terms: bx + -1bx = 0
by = 0 + by
by = by

Add '-1by' to each side of the equation.
by + -1by = by + -1by

Combine like terms: by + -1by = 0
0 = by + -1by

Combine like terms: by + -1by = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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