Multiply polynomial $ \, \color{blue}{ 3x-4 } \, $ by $ \, \color{orangered}{ 3+4x }$.

$$ \left( \color{blue}{3x-4} \right) \cdot \left( \color{orangered}{3+4x} \right) = 12x^2-7x-12 $$

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

$$ \begin{aligned} P(x) &= 3x-4 \\ Q(x) &= 4x+3 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 3x-4}\right) \cdot \left( \color{orangered}{ 4x+3}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{4x} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \color{orangered}{3} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \color{orangered}{4x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \color{orangered}{3} }_{\text{LAST}} = \\ &= 12x^2 + 9x + \left( -16x\right) + \left( -12\right) = \\ &= 12x^2 + 9x + \left( -16x\right) + \left( -12\right) = \\ &= 12x^2-7x-12; \end{aligned} $$

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