Multiply polynomial $ \, \color{blue}{ -8-6i } \, $ by $ \, \color{orangered}{ -8+6i }$.

$$ \left( \color{blue}{-8-6i} \right) \cdot \left( \color{orangered}{-8+6i} \right) = -36i^2+64 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -6i-8 \\ Q(x) &= 6i-8 \\ \end{aligned} $$

In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ -6i-8}\right) \cdot \left( \color{orangered}{ 6i-8}\right) &= \underbrace{ \left( \color{blue}{-6i} \right) \cdot \color{orangered}{6i} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-6i} \right) \cdot \left( \color{orangered}{-8} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-8} \right) \cdot \color{orangered}{6i} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-8} \right) \cdot \left( \color{orangered}{-8} \right) }_{\text{LAST}} = \\ &= -36i^2 + 48i + \left( -48i\right) + 64 = \\ &= -36i^2 + 48i + \left( -48i\right) + 64 = \\ &= -36i^2+64; \end{aligned} $$

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