Answer
$$-(x+4)(x+4)(x-1)(x-1)(x+2)(2x-3)=-2x^6-13x^5-2x^4+83x^3-2x^2-160x+96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-(x+4)(x+4)(x-1)(x-1)(x+2)(2x-3)& \xlongequal{ }-(x^2+4x+4x+16)(x-1)(x-1)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^2+8x+16)(x-1)(x-1)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^3-x^2+8x^2-8x+16x-16)(x-1)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^3+7x^2+8x-16)(x-1)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^4+6x^3+x^2-24x+16)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^5+8x^4+13x^3-22x^2-32x+32)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(2x^6+13x^5+2x^4-83x^3+2x^2+160x-96) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^6-13x^5-2x^4+83x^3-2x^2-160x+96\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^5+8x^4+13x^3-22x^2-32x+32}\right) $ by each term in $ \left( 2x-3\right) $. $$ \left( \color{blue}{x^5+8x^4+13x^3-22x^2-32x+32}\right) \cdot \left( 2x-3\right) = \\ = 2x^6-3x^5+16x^5-24x^4+26x^4-39x^3-44x^3+66x^2-64x^2+96x+64x-96 $$ |
| ② | Combine like terms: $$ 2x^6 \color{blue}{-3x^5} + \color{blue}{16x^5} \color{red}{-24x^4} + \color{red}{26x^4} \color{green}{-39x^3} \color{green}{-44x^3} + \color{orange}{66x^2} \color{orange}{-64x^2} + \color{blue}{96x} + \color{blue}{64x} -96 = \\ = 2x^6+ \color{blue}{13x^5} + \color{red}{2x^4} \color{green}{-83x^3} + \color{orange}{2x^2} + \color{blue}{160x} -96 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^6+13x^5+2x^4-83x^3+2x^2+160x-96 \right) = -2x^6-13x^5-2x^4+83x^3-2x^2-160x+96 $$ |
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