Multiply polynomial $ \, \color{blue}{ 5-9v } \, $ by $ \, \color{orangered}{ 5+9v }$.

$$ \left( \color{blue}{5-9v} \right) \cdot \left( \color{orangered}{5+9v} \right) = -81v^2+25 $$

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

$$ \begin{aligned} P(x) &= -9v+5 \\ Q(x) &= 9v+5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -9v+5}\right) \cdot \left( \color{orangered}{ 9v+5}\right) &= \underbrace{ \left( \color{blue}{-9v} \right) \cdot \color{orangered}{9v} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-9v} \right) \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{9v} }_{\text{INNER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= -81v^2 + \left( -45v\right) + 45v + 25 = \\ &= -81v^2 + \left( -45v\right) + 45v + 25 = \\ &= -81v^2+25; \end{aligned} $$

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