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

$$ \begin{aligned} \left( \color{blue}{ 5x^2-6}\right) \cdot \left( \color{orangered}{ 3x^2-7}\right) &= \underbrace{ \color{blue}{5x^2} \cdot \color{orangered}{3x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{5x^2} \cdot \left( \color{orangered}{-7} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \color{orangered}{3x^2} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \left( \color{orangered}{-7} \right) }_{\text{LAST}} = \\ &= 15x^4 + \left( -35x^2\right) + \left( -18x^2\right) + 42 = \\ &= 15x^4 + \left( -35x^2\right) + \left( -18x^2\right) + 42 = \\ &= 15x^4-53x^2+42; \end{aligned} $$

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