Question
Multiply polynomial $ \, \color{blue}{ 2x^9+3x^7 } \, $ by $ \, \color{orangered}{ -6x^2+9 }$.
Answer
$$ \left( \color{blue}{2x^9+3x^7} \right) \cdot \left( \color{orangered}{-6x^2+9} \right) = -12x^{11}+27x^7 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ 2x^9+3x^7}\right) \cdot \left( \color{orangered}{ -6x^2+9}\right) &= \underbrace{ \color{blue}{2x^9} \cdot \left( \color{orangered}{-6x^2} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{2x^9} \cdot \color{orangered}{9} }_{\text{OUTER}} + \underbrace{ \color{blue}{3x^7} \cdot \left( \color{orangered}{-6x^2} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{3x^7} \cdot \color{orangered}{9} }_{\text{LAST}} = \\ &= -12x^{11} + 18x^9 + \left( -18x^9\right) + 27x^7 = \\ &= -12x^{11} + 18x^9 + \left( -18x^9\right) + 27x^7 = \\ &= -12x^{11}+27x^7; \end{aligned} $$This page was created using
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