Multiply polynomial $ \, \color{blue}{ 4x^2+6 } \, $ by $ \, \color{orangered}{ 2x^2-2 }$.

$$ \left( \color{blue}{4x^2+6} \right) \cdot \left( \color{orangered}{2x^2-2} \right) = 8x^4+4x^2-12 $$

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

$$ \begin{aligned} \left( \color{blue}{ 4x^2+6}\right) \cdot \left( \color{orangered}{ 2x^2-2}\right) &= \underbrace{ \color{blue}{4x^2} \cdot \color{orangered}{2x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x^2} \cdot \left( \color{orangered}{-2} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{6} \cdot \color{orangered}{2x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{6} \cdot \left( \color{orangered}{-2} \right) }_{\text{LAST}} = \\ &= 8x^4 + \left( -8x^2\right) + 12x^2 + \left( -12\right) = \\ &= 8x^4 + \left( -8x^2\right) + 12x^2 + \left( -12\right) = \\ &= 8x^4+4x^2-12; \end{aligned} $$

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