Multiply polynomial $ \, \color{blue}{ 4x+9x-78x-83x-42 } \, $ by $ \, \color{orangered}{ 2x+5 }$.

$$ \left( \color{blue}{4x+9x-78x-83x-42} \right) \cdot \left( \color{orangered}{2x+5} \right) = -296x^2-824x-210 $$

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

$$ \begin{aligned} P(x) &= -148x-42 \\ Q(x) &= 2x+5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -148x-42}\right) \cdot \left( \color{orangered}{ 2x+5}\right) &= \underbrace{ \left( \color{blue}{-148x} \right) \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-148x} \right) \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-42} \right) \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-42} \right) \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= -296x^2 + \left( -740x\right) + \left( -84x\right) + \left( -210\right) = \\ &= -296x^2 + \left( -740x\right) + \left( -84x\right) + \left( -210\right) = \\ &= -296x^2-824x-210; \end{aligned} $$

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