Question
Answer
$$(5x^2-9x+6)(6x^2+5x-9)=30x^4-29x^3-54x^2+111x-54$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x^2-9x+6)(6x^2+5x-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}30x^4-29x^3-54x^2+111x-54\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x^2-9x+6}\right) $ by each term in $ \left( 6x^2+5x-9\right) $. $$ \left( \color{blue}{5x^2-9x+6}\right) \cdot \left( 6x^2+5x-9\right) = 30x^4+25x^3-45x^2-54x^3-45x^2+81x+36x^2+30x-54 $$ |
| ② | Combine like terms: $$ 30x^4+ \color{blue}{25x^3} \color{red}{-45x^2} \color{blue}{-54x^3} \color{green}{-45x^2} + \color{orange}{81x} + \color{green}{36x^2} + \color{orange}{30x} -54 = \\ = 30x^4 \color{blue}{-29x^3} \color{green}{-54x^2} + \color{orange}{111x} -54 $$ |
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