Question
Answer
$$2(x-4)(x^2-3)+(3x+2)^3=29x^3+46x^2+30x+32$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-4)(x^2-3)+(3x+2)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x-4)(x^2-3)+27x^3+54x^2+36x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x-8)(x^2-3)+27x^3+54x^2+36x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3-6x-8x^2+24+27x^3+54x^2+36x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}29x^3+46x^2+30x+32\end{aligned} $$ | |
| ① | Find $ \left(3x+2\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 3x $ and $ B = 2 $. $$ \left(3x+2\right)^3 = \left( 3x \right)^3+3 \cdot \left( 3x \right)^2 \cdot 2 + 3 \cdot 3x \cdot 2^2+2^3 = 27x^3+54x^2+36x+8 $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x-4\right) $ $$ \color{blue}{2} \cdot \left( x-4\right) = 2x-8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x-8}\right) $ by each term in $ \left( x^2-3\right) $. $$ \left( \color{blue}{2x-8}\right) \cdot \left( x^2-3\right) = 2x^3-6x-8x^2+24 $$ |
| ④ | Combine like terms: $$ \color{blue}{2x^3} \color{red}{-6x} \color{green}{-8x^2} + \color{orange}{24} + \color{blue}{27x^3} + \color{green}{54x^2} + \color{red}{36x} + \color{orange}{8} = \\ = \color{blue}{29x^3} + \color{green}{46x^2} + \color{red}{30x} + \color{orange}{32} $$ |
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