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

$$ \begin{aligned} P(x) &= -2x^2+5x \\ Q(x) &= 3x-5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -2x^2+5x}\right) \cdot \left( \color{orangered}{ 3x-5}\right) &= \underbrace{ \left( \color{blue}{-2x^2} \right) \cdot \color{orangered}{3x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-2x^2} \right) \cdot \left( \color{orangered}{-5} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{5x} \cdot \color{orangered}{3x} }_{\text{INNER}} + \underbrace{ \color{blue}{5x} \cdot \left( \color{orangered}{-5} \right) }_{\text{LAST}} = \\ &= -6x^3 + 10x^2 + 15x^2 + \left( -25x\right) = \\ &= -6x^3 + 10x^2 + 15x^2 + \left( -25x\right) = \\ &= -6x^3+25x^2-25x; \end{aligned} $$

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