Question
Multiply polynomial $ \, \color{blue}{ -4x^4+10x } \, $ by $ \, \color{orangered}{ 5x^3-1 }$.
Answer
$$ \left( \color{blue}{-4x^4+10x} \right) \cdot \left( \color{orangered}{5x^3-1} \right) = -20x^7+54x^4-10x $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ -4x^4+10x}\right) \cdot \left( \color{orangered}{ 5x^3-1}\right) &= \underbrace{ \left( \color{blue}{-4x^4} \right) \cdot \color{orangered}{5x^3} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-4x^4} \right) \cdot \left( \color{orangered}{-1} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{10x} \cdot \color{orangered}{5x^3} }_{\text{INNER}} + \underbrace{ \color{blue}{10x} \cdot \left( \color{orangered}{-1} \right) }_{\text{LAST}} = \\ &= -20x^7 + 4x^4 + 50x^4 + \left( -10x\right) = \\ &= -20x^7 + 4x^4 + 50x^4 + \left( -10x\right) = \\ &= -20x^7+54x^4-10x; \end{aligned} $$This page was created using
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