Answer
$$-2(x+2)(x-2)\cdot(1+x)(x-1)=-2x^4+10x^2-8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2(x+2)(x-2)\cdot(1+x)(x-1)& \xlongequal{ }-(2x+4)(x-2)\cdot(1+x)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^2-4x+4x-8)\cdot(1+x)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^2-8)\cdot(1+x)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^2+2x^3-8-8x)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(2x^4-10x^2+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^4+10x^2-8\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^2+2x^3-8-8x}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{2x^2+2x^3-8-8x}\right) \cdot \left( x-1\right) = \\ = \cancel{2x^3}-2x^2+2x^4 -\cancel{2x^3} -\cancel{8x}+8-8x^2+ \cancel{8x} $$ |
| ② | Combine like terms: $$ \, \color{blue}{ \cancel{2x^3}} \, \color{green}{-2x^2} +2x^4 \, \color{blue}{ -\cancel{2x^3}} \, \, \color{orange}{ -\cancel{8x}} \,+8 \color{green}{-8x^2} + \, \color{orange}{ \cancel{8x}} \, = 2x^4 \color{green}{-10x^2} +8 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^4-10x^2+8 \right) = -2x^4+10x^2-8 $$ |
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