Question
Answer
$$10(2\cdot0.6x^3+(6\cdot2\cdot0.1-2\cdot2\cdot0.6)x^2+(6\cdot0.1-12\cdot2)x-12)=-240x-120$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10(2\cdot0.6x^3+(6\cdot2\cdot0.1-2\cdot2\cdot0.6)x^2+(6\cdot0.1-12\cdot2)x-12)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10(2\cdot0.6x^3+(12\cdot0.1-4\cdot0.6)x^2+(6\cdot0.1-24)x-12) \xlongequal{ } \\[1 em] & \xlongequal{ }10(0x^3+(0-0)x^2+(0-24)x-12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10(0x^3+0x^2-24x-12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}0x^3+0x^2-240x-120 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-240x-120\end{aligned} $$ | |
| ① | $$ 6 \cdot 2 = 12 $$$$ 2 \cdot 2 = 4 $$$$ 12 \cdot 2 = 24 $$ |
| ② | Combine like terms: $$ \, \color{blue}{ \cancel{0}} \, \, \color{blue}{ \cancel{0}} \, = \color{blue}{0} $$Combine like terms: $$ \color{blue}{0} \color{blue}{-24} = \color{blue}{-24} $$ |
| ③ | Multiply $ \color{blue}{10} $ by $ \left( 0x^30x^2-24x-12\right) $ $$ \color{blue}{10} \cdot \left( 0x^30x^2-24x-12\right) = 0x^30x^2-240x-120 $$ |
| ④ | Combine like terms: $$ -240x-120 = -240x-120 $$ |
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