Tap the blue circles to see an explanation.
| $$ \begin{aligned}((6-4x)(-5x^2-32)-29(x-1)(xx+3))(2x-3x^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}((6-4x)(-5x^2-32)-29(x-1)(x^2+3))(2x-3x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-30x^2-192+20x^3+128x-(29x-29)(x^2+3))(2x-3x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(-30x^2-192+20x^3+128x-(29x^3+87x-29x^2-87))(2x-3x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(-30x^2-192+20x^3+128x-29x^3-87x+29x^2+87)(2x-3x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(-9x^3-x^2+41x-105)(2x-3x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}27x^5-15x^4-125x^3+397x^2-210x\end{aligned} $$ | |
| ① | $$ x x = x^{1 + 1} = x^2 $$ |
| ② | Multiply each term of $ \left( \color{blue}{6-4x}\right) $ by each term in $ \left( -5x^2-32\right) $. $$ \left( \color{blue}{6-4x}\right) \cdot \left( -5x^2-32\right) = -30x^2-192+20x^3+128x $$Multiply $ \color{blue}{29} $ by $ \left( x-1\right) $ $$ \color{blue}{29} \cdot \left( x-1\right) = 29x-29 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{29x-29}\right) $ by each term in $ \left( x^2+3\right) $. $$ \left( \color{blue}{29x-29}\right) \cdot \left( x^2+3\right) = 29x^3+87x-29x^2-87 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 29x^3+87x-29x^2-87 \right) = -29x^3-87x+29x^2+87 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-30x^2} \color{red}{-192} + \color{green}{20x^3} + \color{orange}{128x} \color{green}{-29x^3} \color{orange}{-87x} + \color{blue}{29x^2} + \color{red}{87} = \\ = \color{green}{-9x^3} \color{blue}{-x^2} + \color{orange}{41x} \color{red}{-105} $$ |
| ⑥ | Multiply each term of $ \left( \color{blue}{-9x^3-x^2+41x-105}\right) $ by each term in $ \left( 2x-3x^2\right) $. $$ \left( \color{blue}{-9x^3-x^2+41x-105}\right) \cdot \left( 2x-3x^2\right) = -18x^4+27x^5-2x^3+3x^4+82x^2-123x^3-210x+315x^2 $$ |
| ⑦ | Combine like terms: $$ \color{blue}{-18x^4} +27x^5 \color{red}{-2x^3} + \color{blue}{3x^4} + \color{green}{82x^2} \color{red}{-123x^3} -210x+ \color{green}{315x^2} = \\ = 27x^5 \color{blue}{-15x^4} \color{red}{-125x^3} + \color{green}{397x^2} -210x $$ |