Question
Answer
$$(x^2+9)(x+2)(2x^2-5x-3)=2x^5-x^4+5x^3-15x^2-117x-54$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+9)(x+2)(2x^2-5x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^3+2x^2+9x+18)(2x^2-5x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^5-x^4+5x^3-15x^2-117x-54\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+9}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x^2+9}\right) \cdot \left( x+2\right) = x^3+2x^2+9x+18 $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^3+2x^2+9x+18}\right) $ by each term in $ \left( 2x^2-5x-3\right) $. $$ \left( \color{blue}{x^3+2x^2+9x+18}\right) \cdot \left( 2x^2-5x-3\right) = \\ = 2x^5-5x^4-3x^3+4x^4-10x^3-6x^2+18x^3-45x^2-27x+36x^2-90x-54 $$ |
| ③ | Combine like terms: $$ 2x^5 \color{blue}{-5x^4} \color{red}{-3x^3} + \color{blue}{4x^4} \color{green}{-10x^3} \color{orange}{-6x^2} + \color{green}{18x^3} \color{blue}{-45x^2} \color{red}{-27x} + \color{blue}{36x^2} \color{red}{-90x} -54 = \\ = 2x^5 \color{blue}{-x^4} + \color{green}{5x^3} \color{blue}{-15x^2} \color{red}{-117x} -54 $$ |
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