Answer
$$-3(x+2)(x-4)(x-2)(x+6)=-3x^4-6x^3+84x^2+24x-288$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3(x+2)(x-4)(x-2)(x+6)& \xlongequal{ }-(3x+6)(x-4)(x-2)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ }-(3x^2-12x+6x-24)(x-2)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ }-(3x^2-6x-24)(x-2)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ }-(3x^3-6x^2-6x^2+12x-24x+48)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ }-(3x^3-12x^2-12x+48)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(3x^4+6x^3-84x^2-24x+288) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-3x^4-6x^3+84x^2+24x-288\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x^3-12x^2-12x+48}\right) $ by each term in $ \left( x+6\right) $. $$ \left( \color{blue}{3x^3-12x^2-12x+48}\right) \cdot \left( x+6\right) = 3x^4+18x^3-12x^3-72x^2-12x^2-72x+48x+288 $$ |
| ② | Combine like terms: $$ 3x^4+ \color{blue}{18x^3} \color{blue}{-12x^3} \color{red}{-72x^2} \color{red}{-12x^2} \color{green}{-72x} + \color{green}{48x} +288 = \\ = 3x^4+ \color{blue}{6x^3} \color{red}{-84x^2} \color{green}{-24x} +288 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(3x^4+6x^3-84x^2-24x+288 \right) = -3x^4-6x^3+84x^2+24x-288 $$ |
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