Question
Answer
$$-4(x-5)^3(x+6)^2=-4x^5+12x^4+276x^3-940x^2-4800x+18000$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-4(x-5)^3(x+6)^2& \xlongequal{ }-4(x^3-15x^2+75x-125)(x^2+12x+36) \xlongequal{ } \\[1 em] & \xlongequal{ }-(4x^3-60x^2+300x-500)(x^2+12x+36) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(4x^5-12x^4-276x^3+940x^2+4800x-18000) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-4x^5+12x^4+276x^3-940x^2-4800x+18000\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4x^3-60x^2+300x-500}\right) $ by each term in $ \left( x^2+12x+36\right) $. $$ \left( \color{blue}{4x^3-60x^2+300x-500}\right) \cdot \left( x^2+12x+36\right) = \\ = 4x^5+48x^4+144x^3-60x^4-720x^3-2160x^2+300x^3+3600x^2+10800x-500x^2-6000x-18000 $$ |
| ② | Combine like terms: $$ 4x^5+ \color{blue}{48x^4} + \color{red}{144x^3} \color{blue}{-60x^4} \color{green}{-720x^3} \color{orange}{-2160x^2} + \color{green}{300x^3} + \color{blue}{3600x^2} + \color{red}{10800x} \color{blue}{-500x^2} \color{red}{-6000x} -18000 = \\ = 4x^5 \color{blue}{-12x^4} \color{green}{-276x^3} + \color{blue}{940x^2} + \color{red}{4800x} -18000 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(4x^5-12x^4-276x^3+940x^2+4800x-18000 \right) = -4x^5+12x^4+276x^3-940x^2-4800x+18000 $$ |
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