Question
Multiply polynomial $ \, \color{blue}{ 3x^2-9x } \, $ by $ \, \color{orangered}{ x^2-9x }$.
Answer
$$ \left( \color{blue}{3x^2-9x} \right) \cdot \left( \color{orangered}{x^2-9x} \right) = 3x^4-36x^3+81x^2 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ 3x^2-9x}\right) \cdot \left( \color{orangered}{ x^2-9x}\right) &= \underbrace{ \color{blue}{3x^2} \cdot \color{orangered}{x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x^2} \cdot \left( \color{orangered}{-9x} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-9x} \right) \cdot \color{orangered}{x^2} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-9x} \right) \cdot \left( \color{orangered}{-9x} \right) }_{\text{LAST}} = \\ &= 3x^4 + \left( -27x^3\right) + \left( -9x^3\right) + 81x^2 = \\ &= 3x^4 + \left( -27x^3\right) + \left( -9x^3\right) + 81x^2 = \\ &= 3x^4-36x^3+81x^2; \end{aligned} $$This page was created using
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