Multiply polynomial $ \, \color{blue}{ 6x^2-30x } \, $ by $ \, \color{orangered}{ x+5 }$.

$$ \left( \color{blue}{6x^2-30x} \right) \cdot \left( \color{orangered}{x+5} \right) = 6x^3-150x $$

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

$$ \begin{aligned} \left( \color{blue}{ 6x^2-30x}\right) \cdot \left( \color{orangered}{ x+5}\right) &= \underbrace{ \color{blue}{6x^2} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{6x^2} \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-30x} \right) \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-30x} \right) \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= 6x^3 + 30x^2 + \left( -30x^2\right) + \left( -150x\right) = \\ &= 6x^3 + 30x^2 + \left( -30x^2\right) + \left( -150x\right) = \\ &= 6x^3-150x; \end{aligned} $$

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