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

$$ \left( \color{blue}{-8x^6+8} \right) \cdot \left( \color{orangered}{-8x^6-8x} \right) = 64x^{12}+64x^7-64x^6-64x $$

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

$$ \begin{aligned} \left( \color{blue}{ -8x^6+8}\right) \cdot \left( \color{orangered}{ -8x^6-8x}\right) &= \underbrace{ \left( \color{blue}{-8x^6} \right) \cdot \left( \color{orangered}{-8x^6} \right) }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-8x^6} \right) \cdot \left( \color{orangered}{-8x} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{8} \cdot \left( \color{orangered}{-8x^6} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{8} \cdot \left( \color{orangered}{-8x} \right) }_{\text{LAST}} = \\ &= 64x^{12} + 64x^7 + \left( -64x^6\right) + \left( -64x\right) = \\ &= 64x^{12} + 64x^7 + \left( -64x^6\right) + \left( -64x\right) = \\ &= 64x^{12}+64x^7-64x^6-64x; \end{aligned} $$

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