Multiply polynomial $ \, \color{blue}{ 5+3x+2x } \, $ by $ \, \color{orangered}{ 2x+5 }$.

$$ \left( \color{blue}{5+3x+2x} \right) \cdot \left( \color{orangered}{2x+5} \right) = 10x^2+35x+25 $$

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

$$ \begin{aligned} P(x) &= 5x+5 \\ Q(x) &= 2x+5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 5x+5}\right) \cdot \left( \color{orangered}{ 2x+5}\right) &= \underbrace{ \color{blue}{5x} \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \color{blue}{5x} \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= 10x^2 + 25x + 10x + 25 = \\ &= 10x^2 + 25x + 10x + 25 = \\ &= 10x^2+35x+25; \end{aligned} $$

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