Multiply polynomial $ \, \color{blue}{ 2x+5 } \, $ by $ \, \color{orangered}{ x^2-7 }$.

$$ \left( \color{blue}{2x+5} \right) \cdot \left( \color{orangered}{x^2-7} \right) = 2x^3+5x^2-14x-35 $$

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

$$ \begin{aligned} \left( \color{blue}{ 2x+5}\right) \cdot \left( \color{orangered}{ x^2-7}\right) &= \underbrace{ \color{blue}{2x} \cdot \color{orangered}{x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-7} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{5} \cdot \left( \color{orangered}{-7} \right) }_{\text{LAST}} = \\ &= 2x^3 + \left( -14x\right) + 5x^2 + \left( -35\right) = \\ &= 2x^3 + \left( -14x\right) + 5x^2 + \left( -35\right) = \\ &= 2x^3+5x^2-14x-35; \end{aligned} $$

Polynomial Operations Calculator