Question
Answer
$$-6x^2(x^3-1)^2-6x^2(-2x^3-1)(x^3-1)=6x^8+6x^5-12x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-6x^2(x^3-1)^2-6x^2(-2x^3-1)(x^3-1)& \xlongequal{ }-6x^2(x^6-2x^3+1)-6x^2(-2x^3-1)(x^3-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(6x^8-12x^5+6x^2)-(-12x^5-6x^2)(x^3-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-6x^8+12x^5-6x^2-(-12x^5-6x^2)(x^3-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-6x^8+12x^5-6x^2-(-12x^8+12x^5-6x^5+6x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-6x^8+12x^5-6x^2-(-12x^8+6x^5+6x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-6x^8+12x^5-6x^2+12x^8-6x^5-6x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}6x^8+6x^5-12x^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{6x^2} $ by $ \left( x^6-2x^3+1\right) $ $$ \color{blue}{6x^2} \cdot \left( x^6-2x^3+1\right) = 6x^8-12x^5+6x^2 $$Multiply $ \color{blue}{6x^2} $ by $ \left( -2x^3-1\right) $ $$ \color{blue}{6x^2} \cdot \left( -2x^3-1\right) = -12x^5-6x^2 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(6x^8-12x^5+6x^2 \right) = -6x^8+12x^5-6x^2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{-12x^5-6x^2}\right) $ by each term in $ \left( x^3-1\right) $. $$ \left( \color{blue}{-12x^5-6x^2}\right) \cdot \left( x^3-1\right) = -12x^8+12x^5-6x^5+6x^2 $$ |
| ④ | Combine like terms: $$ -12x^8+ \color{blue}{12x^5} \color{blue}{-6x^5} +6x^2 = -12x^8+ \color{blue}{6x^5} +6x^2 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -12x^8+6x^5+6x^2 \right) = 12x^8-6x^5-6x^2 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{-6x^8} + \color{red}{12x^5} \color{green}{-6x^2} + \color{blue}{12x^8} \color{red}{-6x^5} \color{green}{-6x^2} = \color{blue}{6x^8} + \color{red}{6x^5} \color{green}{-12x^2} $$ |
This page was created using
Simplify Rational Expressions