Multiply polynomial $ \, \color{blue}{ 3+4c } \, $ by $ \, \color{orangered}{ 6+5c }$.

$$ \left( \color{blue}{3+4c} \right) \cdot \left( \color{orangered}{6+5c} \right) = 20c^2+39c+18 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 4c+3 \\ Q(x) &= 5c+6 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 4c+3}\right) \cdot \left( \color{orangered}{ 5c+6}\right) &= \underbrace{ \color{blue}{4c} \cdot \color{orangered}{5c} }_{\text{FIRST}} + \underbrace{ \color{blue}{4c} \cdot \color{orangered}{6} }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{5c} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{6} }_{\text{LAST}} = \\ &= 20c^2 + 24c + 15c + 18 = \\ &= 20c^2 + 24c + 15c + 18 = \\ &= 20c^2+39c+18; \end{aligned} $$

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