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

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

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