Question
Answer
$$(x^2+x-1)(2x^2+5x-9)=2x^4+7x^3-6x^2-14x+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+x-1)(2x^2+5x-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^4+7x^3-6x^2-14x+9\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+x-1}\right) $ by each term in $ \left( 2x^2+5x-9\right) $. $$ \left( \color{blue}{x^2+x-1}\right) \cdot \left( 2x^2+5x-9\right) = 2x^4+5x^3-9x^2+2x^3+5x^2-9x-2x^2-5x+9 $$ |
| ② | Combine like terms: $$ 2x^4+ \color{blue}{5x^3} \color{red}{-9x^2} + \color{blue}{2x^3} + \color{green}{5x^2} \color{orange}{-9x} \color{green}{-2x^2} \color{orange}{-5x} +9 = \\ = 2x^4+ \color{blue}{7x^3} \color{green}{-6x^2} \color{orange}{-14x} +9 $$ |
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