Question
Multiply polynomial $ \, \color{blue}{ -3x^2-4 } \, $ by $ \, \color{orangered}{ 2x-1 }$.
Answer
$$ \left( \color{blue}{-3x^2-4} \right) \cdot \left( \color{orangered}{2x-1} \right) = -6x^3+3x^2-8x+4 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ -3x^2-4}\right) \cdot \left( \color{orangered}{ 2x-1}\right) &= \underbrace{ \left( \color{blue}{-3x^2} \right) \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-3x^2} \right) \cdot \left( \color{orangered}{-1} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \left( \color{orangered}{-1} \right) }_{\text{LAST}} = \\ &= -6x^3 + 3x^2 + \left( -8x\right) + 4 = \\ &= -6x^3 + 3x^2 + \left( -8x\right) + 4 = \\ &= -6x^3+3x^2-8x+4; \end{aligned} $$This page was created using
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