Question
Answer
$$672x^3+(x+2)^3-2(10x+3x^3)=667x^3+6x^2-8x+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}672x^3+(x+2)^3-2(10x+3x^3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}672x^3+x^3+6x^2+12x+8-2(10x+3x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}673x^3+6x^2+12x+8-2(10x+3x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}673x^3+6x^2+12x+8-(20x+6x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}673x^3+6x^2+12x+8-20x-6x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}667x^3+6x^2-8x+8\end{aligned} $$ | |
| ① | Find $ \left(x+2\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = x $ and $ B = 2 $. $$ \left(x+2\right)^3 = x^3+3 \cdot x^2 \cdot 2 + 3 \cdot x \cdot 2^2+2^3 = x^3+6x^2+12x+8 $$ |
| ② | Combine like terms: $$ \color{blue}{672x^3} + \color{blue}{x^3} +6x^2+12x+8 = \color{blue}{673x^3} +6x^2+12x+8 $$ |
| ③ | Multiply $ \color{blue}{2} $ by $ \left( 10x+3x^3\right) $ $$ \color{blue}{2} \cdot \left( 10x+3x^3\right) = 20x+6x^3 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 20x+6x^3 \right) = -20x-6x^3 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{673x^3} +6x^2+ \color{red}{12x} +8 \color{red}{-20x} \color{blue}{-6x^3} = \color{blue}{667x^3} +6x^2 \color{red}{-8x} +8 $$ |
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