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

$$ \left( \color{blue}{y+3} \right) \cdot \left( \color{orangered}{y+5} \right) = y^2+8y+15 $$

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

$$ \begin{aligned} \left( \color{blue}{ y+3}\right) \cdot \left( \color{orangered}{ y+5}\right) &= \underbrace{ \color{blue}{y} \cdot \color{orangered}{y} }_{\text{FIRST}} + \underbrace{ \color{blue}{y} \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{y} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= y^2 + 5y + 3y + 15 = \\ &= y^2 + 5y + 3y + 15 = \\ &= y^2+8y+15; \end{aligned} $$

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