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

$$ \begin{aligned} \left( \color{blue}{ 4x^2-8}\right) \cdot \left( \color{orangered}{ -10x^2+2}\right) &= \underbrace{ \color{blue}{4x^2} \cdot \left( \color{orangered}{-10x^2} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{4x^2} \cdot \color{orangered}{2} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-8} \right) \cdot \left( \color{orangered}{-10x^2} \right) }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-8} \right) \cdot \color{orangered}{2} }_{\text{LAST}} = \\ &= -40x^4 + 8x^2 + 80x^2 + \left( -16\right) = \\ &= -40x^4 + 8x^2 + 80x^2 + \left( -16\right) = \\ &= -40x^4+88x^2-16; \end{aligned} $$

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