(x-4i)(x+4i)(x-4-i)(x-4+i)=P(x)

Simple and best practice solution for (x-4i)(x+4i)(x-4-i)(x-4+i)=P(x) 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.

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Solution for (x-4i)(x+4i)(x-4-i)(x-4+i)=P(x) equation:

Simplifying
(x + -4i)(x + 4i)(x + -4 + -1i)(x + -4 + i) = P(x)

Reorder the terms:
(-4i + x)(x + 4i)(x + -4 + -1i)(x + -4 + i) = P(x)

Reorder the terms:
(-4i + x)(4i + x)(x + -4 + -1i)(x + -4 + i) = P(x)

Reorder the terms:
(-4i + x)(4i + x)(-4 + -1i + x)(x + -4 + i) = P(x)

Reorder the terms:
(-4i + x)(4i + x)(-4 + -1i + x)(-4 + i + x) = P(x)

Multiply (-4i + x) * (4i + x)
(-4i * (4i + x) + x(4i + x))(-4 + -1i + x)(-4 + i + x) = P(x)
((4i * -4i + x * -4i) + x(4i + x))(-4 + -1i + x)(-4 + i + x) = P(x)

Reorder the terms:
((-4ix + -16i²) + x(4i + x))(-4 + -1i + x)(-4 + i + x) = P(x)
((-4ix + -16i²) + x(4i + x))(-4 + -1i + x)(-4 + i + x) = P(x)
(-4ix + -16i² + (4i * x + x * x))(-4 + -1i + x)(-4 + i + x) = P(x)
(-4ix + -16i² + (4ix + x²))(-4 + -1i + x)(-4 + i + x) = P(x)

Reorder the terms:
(-4ix + 4ix + -16i² + x²)(-4 + -1i + x)(-4 + i + x) = P(x)

Combine like terms: -4ix + 4ix = 0
(0 + -16i² + x²)(-4 + -1i + x)(-4 + i + x) = P(x)
(-16i² + x²)(-4 + -1i + x)(-4 + i + x) = P(x)

Multiply (-16i² + x²) * (-4 + -1i + x)
(-16i² * (-4 + -1i + x) + x²(-4 + -1i + x))(-4 + i + x) = P(x)
((-4 * -16i² + -1i * -16i² + x * -16i²) + x²(-4 + -1i + x))(-4 + i + x) = P(x)

Reorder the terms:
((64i² + -16i²x + 16i³) + x²(-4 + -1i + x))(-4 + i + x) = P(x)
((64i² + -16i²x + 16i³) + x²(-4 + -1i + x))(-4 + i + x) = P(x)
(64i² + -16i²x + 16i³ + (-4 * x² + -1i * x² + x * x²))(-4 + i + x) = P(x)

Reorder the terms:
(64i² + -16i²x + 16i³ + (-1ix² + -4x² + x³))(-4 + i + x) = P(x)
(64i² + -16i²x + 16i³ + (-1ix² + -4x² + x³))(-4 + i + x) = P(x)

Reorder the terms:
(-1ix² + 64i² + -16i²x + 16i³ + -4x² + x³)(-4 + i + x) = P(x)
(-1ix² + 64i² + -16i²x + 16i³ + -4x² + x³)(-4 + i + x) = P(x)

Multiply (-1ix² + 64i² + -16i²x + 16i³ + -4x² + x³) * (-4 + i + x)
(-1ix² * (-4 + i + x) + 64i² * (-4 + i + x) + -16i²x * (-4 + i + x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
((-4 * -1ix² + i * -1ix² + x * -1ix²) + 64i² * (-4 + i + x) + -16i²x * (-4 + i + x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)

Reorder the terms:
((4ix² + -1ix³ + -1i²x²) + 64i² * (-4 + i + x) + -16i²x * (-4 + i + x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
((4ix² + -1ix³ + -1i²x²) + 64i² * (-4 + i + x) + -16i²x * (-4 + i + x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + (-4 * 64i² + i * 64i² + x * 64i²) + -16i²x * (-4 + i + x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)

Reorder the terms:
(4ix² + -1ix³ + -1i²x² + (-256i² + 64i²x + 64i³) + -16i²x * (-4 + i + x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + (-256i² + 64i²x + 64i³) + -16i²x * (-4 + i + x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + (-4 * -16i²x + i * -16i²x + x * -16i²x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)

Reorder the terms:
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + (64i²x + -16i²x² + -16i³x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + (64i²x + -16i²x² + -16i³x) + 16i³ * (-4 + i + x) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + (-4 * 16i³ + i * 16i³ + x * 16i³) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)

Reorder the terms:
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + (-64i³ + 16i³x + 16i⁴) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + (-64i³ + 16i³x + 16i⁴) + -4x² * (-4 + i + x) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + -64i³ + 16i³x + 16i⁴ + (-4 * -4x² + i * -4x² + x * -4x²) + x³(-4 + i + x)) = P(x)

Reorder the terms:
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + -64i³ + 16i³x + 16i⁴ + (-4ix² + 16x² + -4x³) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + -64i³ + 16i³x + 16i⁴ + (-4ix² + 16x² + -4x³) + x³(-4 + i + x)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + -64i³ + 16i³x + 16i⁴ + -4ix² + 16x² + -4x³ + (-4 * x³ + i * x³ + x * x³)) = P(x)

Reorder the terms:
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + -64i³ + 16i³x + 16i⁴ + -4ix² + 16x² + -4x³ + (ix³ + -4x³ + x⁴)) = P(x)
(4ix² + -1ix³ + -1i²x² + -256i² + 64i²x + 64i³ + 64i²x + -16i²x² + -16i³x + -64i³ + 16i³x + 16i⁴ + -4ix² + 16x² + -4x³ + (ix³ + -4x³ + x⁴)) = P(x)

Reorder the terms:
(4ix² + -4ix² + -1ix³ + ix³ + -256i² + 64i²x + 64i²x + -1i²x² + -16i²x² + 64i³ + -64i³ + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)

Combine like terms: 4ix² + -4ix² = 0
(0 + -1ix³ + ix³ + -256i² + 64i²x + 64i²x + -1i²x² + -16i²x² + 64i³ + -64i³ + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)
(-1ix³ + ix³ + -256i² + 64i²x + 64i²x + -1i²x² + -16i²x² + 64i³ + -64i³ + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)

Combine like terms: -1ix³ + ix³ = 0
(0 + -256i² + 64i²x + 64i²x + -1i²x² + -16i²x² + 64i³ + -64i³ + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)
(-256i² + 64i²x + 64i²x + -1i²x² + -16i²x² + 64i³ + -64i³ + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)

Combine like terms: 64i²x + 64i²x = 128i²x
(-256i² + 128i²x + -1i²x² + -16i²x² + 64i³ + -64i³ + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)

Combine like terms: -1i²x² + -16i²x² = -17i²x²
(-256i² + 128i²x + -17i²x² + 64i³ + -64i³ + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)

Combine like terms: 64i³ + -64i³ = 0
(-256i² + 128i²x + -17i²x² + 0 + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)
(-256i² + 128i²x + -17i²x² + -16i³x + 16i³x + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)

Combine like terms: -16i³x + 16i³x = 0
(-256i² + 128i²x + -17i²x² + 0 + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)
(-256i² + 128i²x + -17i²x² + 16i⁴ + 16x² + -4x³ + -4x³ + x⁴) = P(x)

Combine like terms: -4x³ + -4x³ = -8x³
(-256i² + 128i²x + -17i²x² + 16i⁴ + 16x² + -8x³ + x⁴) = P(x)

Multiply P * x
-256i² + 128i²x + -17i²x² + 16i⁴ + 16x² + -8x³ + x⁴ = xP

Solving
-256i² + 128i²x + -17i²x² + 16i⁴ + 16x² + -8x³ + x⁴ = xP

Solving for variable 'i'.

Reorder the terms:
-256i² + 128i²x + -17i²x² + 16i⁴ + -1xP + 16x² + -8x³ + x⁴ = xP + -1xP

Combine like terms: xP + -1xP = 0
-256i² + 128i²x + -17i²x² + 16i⁴ + -1xP + 16x² + -8x³ + x⁴ = 0

The solution to this equation could not be determined.

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(x-4i)(x+4i)(x-4-i)(x-4+i)=P(x)

Simple and best practice solution for (x-4i)(x+4i)(x-4-i)(x-4+i)=P(x) 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 (x-4i)(x+4i)(x-4-i)(x-4+i)=P(x) equation:

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