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

$$ \left( \color{blue}{x^2+2x+x} \right) \cdot \left( \color{orangered}{x+3} \right) = x^3+6x^2+9x $$

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

$$ \begin{aligned} P(x) &= x^2+3x \\ Q(x) &= x+3 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ x^2+3x}\right) \cdot \left( \color{orangered}{ x+3}\right) &= \underbrace{ \color{blue}{x^2} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{x^2} \cdot \color{orangered}{3} }_{\text{OUTER}} + \underbrace{ \color{blue}{3x} \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \color{blue}{3x} \cdot \color{orangered}{3} }_{\text{LAST}} = \\ &= x^3 + 3x^2 + 3x^2 + 9x = \\ &= x^3 + 3x^2 + 3x^2 + 9x = \\ &= x^3+6x^2+9x; \end{aligned} $$

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