Question
Answer
$$(2x^3-3x^2-11x+6)^2=4x^6-12x^5-35x^4+90x^3+85x^2-132x+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x^3-3x^2-11x+6)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^6-12x^5-35x^4+90x^3+85x^2-132x+36\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^3-3x^2-11x+6}\right) $ by each term in $ \left( 2x^3-3x^2-11x+6\right) $. $$ \left( \color{blue}{2x^3-3x^2-11x+6}\right) \cdot \left( 2x^3-3x^2-11x+6\right) = \\ = 4x^6-6x^5-22x^4+12x^3-6x^5+9x^4+33x^3-18x^2-22x^4+33x^3+121x^2-66x+12x^3-18x^2-66x+36 $$ |
| ② | Combine like terms: $$ 4x^6 \color{blue}{-6x^5} \color{red}{-22x^4} + \color{green}{12x^3} \color{blue}{-6x^5} + \color{orange}{9x^4} + \color{blue}{33x^3} \color{red}{-18x^2} \color{orange}{-22x^4} + \color{green}{33x^3} + \color{orange}{121x^2} \color{blue}{-66x} + \color{green}{12x^3} \color{orange}{-18x^2} \color{blue}{-66x} +36 = \\ = 4x^6 \color{blue}{-12x^5} \color{orange}{-35x^4} + \color{green}{90x^3} + \color{orange}{85x^2} \color{blue}{-132x} +36 $$ |
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