(x-6)(x-4i)(x+4i) In Standard Form

Jasonbradley

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Jun 17, 2024

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Expanding (x - 6)(x - 4i)(x + 4i) into Standard Form

This problem involves expanding a product of three factors, one linear and two complex conjugates. To achieve this, we'll use the distributive property and the knowledge that multiplying a complex number by its conjugate results in a real number.

Steps:

1. Multiply the complex conjugates: (x - 4i)(x + 4i) = x² - (4i)² = x² + 16

2. Multiply the result by the linear term: (x² + 16)(x - 6) = x³ - 6x² + 16x - 96

Final Answer:

The standard form of the expanded expression is x³ - 6x² + 16x - 96.

Key Point: The product of complex conjugates always results in a real number. This is a crucial concept in working with complex numbers.