Question
Multiply polynomial $ \, \color{blue}{ -8x^2-9 } \, $ by $ \, \color{orangered}{ -5x^2+5x }$.
Answer
$$ \left( \color{blue}{-8x^2-9} \right) \cdot \left( \color{orangered}{-5x^2+5x} \right) = 40x^4-40x^3+45x^2-45x $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ -8x^2-9}\right) \cdot \left( \color{orangered}{ -5x^2+5x}\right) &= \underbrace{ \left( \color{blue}{-8x^2} \right) \cdot \left( \color{orangered}{-5x^2} \right) }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-8x^2} \right) \cdot \color{orangered}{5x} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-9} \right) \cdot \left( \color{orangered}{-5x^2} \right) }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-9} \right) \cdot \color{orangered}{5x} }_{\text{LAST}} = \\ &= 40x^4 + \left( -40x^3\right) + 45x^2 + \left( -45x\right) = \\ &= 40x^4 + \left( -40x^3\right) + 45x^2 + \left( -45x\right) = \\ &= 40x^4-40x^3+45x^2-45x; \end{aligned} $$This page was created using
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