Multiply polynomial $ \, \color{blue}{ x+7 } \, $ by $ \, \color{orangered}{ 3x+5 }$.

$$ \left( \color{blue}{x+7} \right) \cdot \left( \color{orangered}{3x+5} \right) = 3x^2+26x+35 $$

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

$$ \begin{aligned} \left( \color{blue}{ x+7}\right) \cdot \left( \color{orangered}{ 3x+5}\right) &= \underbrace{ \color{blue}{x} \cdot \color{orangered}{3x} }_{\text{FIRST}} + \underbrace{ \color{blue}{x} \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \color{blue}{7} \cdot \color{orangered}{3x} }_{\text{INNER}} + \underbrace{ \color{blue}{7} \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= 3x^2 + 5x + 21x + 35 = \\ &= 3x^2 + 5x + 21x + 35 = \\ &= 3x^2+26x+35; \end{aligned} $$

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