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

$$ \begin{aligned} \left( \color{blue}{ -5x+6}\right) \cdot \left( \color{orangered}{ 5x+2}\right) &= \underbrace{ \left( \color{blue}{-5x} \right) \cdot \color{orangered}{5x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-5x} \right) \cdot \color{orangered}{2} }_{\text{OUTER}} + \underbrace{ \color{blue}{6} \cdot \color{orangered}{5x} }_{\text{INNER}} + \underbrace{ \color{blue}{6} \cdot \color{orangered}{2} }_{\text{LAST}} = \\ &= -25x^2 + \left( -10x\right) + 30x + 12 = \\ &= -25x^2 + \left( -10x\right) + 30x + 12 = \\ &= -25x^2+20x+12; \end{aligned} $$

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