Multiply polynomial $ \, \color{blue}{ 4x^2+3x } \, $ by $ \, \color{orangered}{ 7x^2-2x }$.

$$ \left( \color{blue}{4x^2+3x} \right) \cdot \left( \color{orangered}{7x^2-2x} \right) = 28x^4+13x^3-6x^2 $$

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

$$ \begin{aligned} \left( \color{blue}{ 4x^2+3x}\right) \cdot \left( \color{orangered}{ 7x^2-2x}\right) &= \underbrace{ \color{blue}{4x^2} \cdot \color{orangered}{7x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x^2} \cdot \left( \color{orangered}{-2x} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{3x} \cdot \color{orangered}{7x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-2x} \right) }_{\text{LAST}} = \\ &= 28x^4 + \left( -8x^3\right) + 21x^3 + \left( -6x^2\right) = \\ &= 28x^4 + \left( -8x^3\right) + 21x^3 + \left( -6x^2\right) = \\ &= 28x^4+13x^3-6x^2; \end{aligned} $$

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