(a-c)(b-c)(a+d)(b+d)=p^2+q^2

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Solution for (a-c)(b-c)(a+d)(b+d)=p^2+q^2 equation:

Simplifying
(a + -1c)(b + -1c)(a + d)(b + d) = p² + q²

Multiply (a + -1c) * (b + -1c)
(a(b + -1c) + -1c * (b + -1c))(a + d)(b + d) = p² + q²
((b * a + -1c * a) + -1c * (b + -1c))(a + d)(b + d) = p² + q²
((ab + -1ac) + -1c * (b + -1c))(a + d)(b + d) = p² + q²
(ab + -1ac + (b * -1c + -1c * -1c))(a + d)(b + d) = p² + q²
(ab + -1ac + (-1bc + 1c²))(a + d)(b + d) = p² + q²
(ab + -1ac + -1bc + 1c²)(a + d)(b + d) = p² + q²

Multiply (ab + -1ac + -1bc + 1c²) * (a + d)
(ab(a + d) + -1ac * (a + d) + -1bc * (a + d) + 1c² * (a + d))(b + d) = p² + q²
((a * ab + d * ab) + -1ac * (a + d) + -1bc * (a + d) + 1c² * (a + d))(b + d) = p² + q²

Reorder the terms:
((abd + a²b) + -1ac * (a + d) + -1bc * (a + d) + 1c² * (a + d))(b + d) = p² + q²
((abd + a²b) + -1ac * (a + d) + -1bc * (a + d) + 1c² * (a + d))(b + d) = p² + q²
(abd + a²b + (a * -1ac + d * -1ac) + -1bc * (a + d) + 1c² * (a + d))(b + d) = p² + q²

Reorder the terms:
(abd + a²b + (-1acd + -1a²c) + -1bc * (a + d) + 1c² * (a + d))(b + d) = p² + q²
(abd + a²b + (-1acd + -1a²c) + -1bc * (a + d) + 1c² * (a + d))(b + d) = p² + q²
(abd + a²b + -1acd + -1a²c + (a * -1bc + d * -1bc) + 1c² * (a + d))(b + d) = p² + q²
(abd + a²b + -1acd + -1a²c + (-1abc + -1bcd) + 1c² * (a + d))(b + d) = p² + q²
(abd + a²b + -1acd + -1a²c + -1abc + -1bcd + (a * 1c² + d * 1c²))(b + d) = p² + q²
(abd + a²b + -1acd + -1a²c + -1abc + -1bcd + (1ac² + 1c²d))(b + d) = p² + q²

Reorder the terms:
(-1abc + abd + -1acd + 1ac² + a²b + -1a²c + -1bcd + 1c²d)(b + d) = p² + q²
(-1abc + abd + -1acd + 1ac² + a²b + -1a²c + -1bcd + 1c²d)(b + d) = p² + q²

Multiply (-1abc + abd + -1acd + 1ac² + a²b + -1a²c + -1bcd + 1c²d) * (b + d)
(-1abc * (b + d) + abd(b + d) + -1acd * (b + d) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
((b * -1abc + d * -1abc) + abd(b + d) + -1acd * (b + d) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²

Reorder the terms:
((-1abcd + -1ab²c) + abd(b + d) + -1acd * (b + d) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
((-1abcd + -1ab²c) + abd(b + d) + -1acd * (b + d) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + (b * abd + d * abd) + -1acd * (b + d) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²

Reorder the terms:
(-1abcd + -1ab²c + (abd² + ab²d) + -1acd * (b + d) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + (abd² + ab²d) + -1acd * (b + d) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + (b * -1acd + d * -1acd) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + (-1abcd + -1acd²) + 1ac² * (b + d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + (b * 1ac² + d * 1ac²) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + (1abc² + 1ac²d) + a²b(b + d) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + (b * a²b + d * a²b) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²

Reorder the terms:
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + (a²bd + a²b²) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + (a²bd + a²b²) + -1a²c * (b + d) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + a²bd + a²b² + (b * -1a²c + d * -1a²c) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + a²bd + a²b² + (-1a²bc + -1a²cd) + -1bcd * (b + d) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + a²bd + a²b² + -1a²bc + -1a²cd + (b * -1bcd + d * -1bcd) + 1c²d * (b + d)) = p² + q²

Reorder the terms:
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + a²bd + a²b² + -1a²bc + -1a²cd + (-1bcd² + -1b²cd) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + a²bd + a²b² + -1a²bc + -1a²cd + (-1bcd² + -1b²cd) + 1c²d * (b + d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + a²bd + a²b² + -1a²bc + -1a²cd + -1bcd² + -1b²cd + (b * 1c²d + d * 1c²d)) = p² + q²
(-1abcd + -1ab²c + abd² + ab²d + -1abcd + -1acd² + 1abc² + 1ac²d + a²bd + a²b² + -1a²bc + -1a²cd + -1bcd² + -1b²cd + (1bc²d + 1c²d²)) = p² + q²

Reorder the terms:
(-1abcd + -1abcd + 1abc² + abd² + -1ab²c + ab²d + -1acd² + 1ac²d + -1a²bc + a²bd + a²b² + -1a²cd + -1bcd² + 1bc²d + -1b²cd + 1c²d²) = p² + q²

Combine like terms: -1abcd + -1abcd = -2abcd
(-2abcd + 1abc² + abd² + -1ab²c + ab²d + -1acd² + 1ac²d + -1a²bc + a²bd + a²b² + -1a²cd + -1bcd² + 1bc²d + -1b²cd + 1c²d²) = p² + q²

Solving
-2abcd + 1abc² + abd² + -1ab²c + ab²d + -1acd² + 1ac²d + -1a²bc + a²bd + a²b² + -1a²cd + -1bcd² + 1bc²d + -1b²cd + 1c²d² = p² + q²

Solving for variable 'a'.

Reorder the terms:
-2abcd + 1abc² + abd² + -1ab²c + ab²d + -1acd² + 1ac²d + -1a²bc + a²bd + a²b² + -1a²cd + -1bcd² + 1bc²d + -1b²cd + 1c²d² + -1p² + -1q² = p² + -1p² + q² + -1q²

Combine like terms: p² + -1p² = 0
-2abcd + 1abc² + abd² + -1ab²c + ab²d + -1acd² + 1ac²d + -1a²bc + a²bd + a²b² + -1a²cd + -1bcd² + 1bc²d + -1b²cd + 1c²d² + -1p² + -1q² = 0 + q² + -1q²
-2abcd + 1abc² + abd² + -1ab²c + ab²d + -1acd² + 1ac²d + -1a²bc + a²bd + a²b² + -1a²cd + -1bcd² + 1bc²d + -1b²cd + 1c²d² + -1p² + -1q² = q² + -1q²

Combine like terms: q² + -1q² = 0
-2abcd + 1abc² + abd² + -1ab²c + ab²d + -1acd² + 1ac²d + -1a²bc + a²bd + a²b² + -1a²cd + -1bcd² + 1bc²d + -1b²cd + 1c²d² + -1p² + -1q² = 0

The solution to this equation could not be determined.

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(a-c)(b-c)(a+d)(b+d)=p^2+q^2

Simple and best practice solution for (a-c)(b-c)(a+d)(b+d)=p^2+q^2 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for (a-c)(b-c)(a+d)(b+d)=p^2+q^2 equation:

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