Question
Multiply polynomial $ \, \color{blue}{ -x-4 } \, $ by $ \, \color{orangered}{ x^6-1 }$.
Answer
$$ \left( \color{blue}{-x-4} \right) \cdot \left( \color{orangered}{x^6-1} \right) = -x^7-4x^6+x+4 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ -x-4}\right) \cdot \left( \color{orangered}{ x^6-1}\right) &= \underbrace{ \left( \color{blue}{-x} \right) \cdot \color{orangered}{x^6} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-x} \right) \cdot \left( \color{orangered}{-1} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \color{orangered}{x^6} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \left( \color{orangered}{-1} \right) }_{\text{LAST}} = \\ &= -x^7 + x + \left( -4x^6\right) + 4 = \\ &= -x^7 + x + \left( -4x^6\right) + 4 = \\ &= -x^7-4x^6+x+4; \end{aligned} $$This page was created using
Polynomial Operations Calculator