Question
Multiply polynomial $ \, \color{blue}{ -9x^5+2x^3 } \, $ by $ \, \color{orangered}{ 9x^3+11x }$.
Answer
$$ \left( \color{blue}{-9x^5+2x^3} \right) \cdot \left( \color{orangered}{9x^3+11x} \right) = -81x^8-81x^6+22x^4 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ -9x^5+2x^3}\right) \cdot \left( \color{orangered}{ 9x^3+11x}\right) &= \underbrace{ \left( \color{blue}{-9x^5} \right) \cdot \color{orangered}{9x^3} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-9x^5} \right) \cdot \color{orangered}{11x} }_{\text{OUTER}} + \underbrace{ \color{blue}{2x^3} \cdot \color{orangered}{9x^3} }_{\text{INNER}} + \underbrace{ \color{blue}{2x^3} \cdot \color{orangered}{11x} }_{\text{LAST}} = \\ &= -81x^8 + \left( -99x^6\right) + 18x^6 + 22x^4 = \\ &= -81x^8 + \left( -99x^6\right) + 18x^6 + 22x^4 = \\ &= -81x^8-81x^6+22x^4; \end{aligned} $$This page was created using
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