Question
Answer
$$3x(x+2)^2+(x+2)^3=4x^3+18x^2+24x+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3x(x+2)^2+(x+2)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3x(x^2+4x+4)+x^3+6x^2+12x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^3+12x^2+12x+x^3+6x^2+12x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^3+18x^2+24x+8\end{aligned} $$ | |
| ① | Find $ \left(x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x+2\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2 + \color{red}{2^2} = x^2+4x+4\end{aligned} $$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 | Multiply $ \color{blue}{3x} $ by $ \left( x^2+4x+4\right) $ $$ \color{blue}{3x} \cdot \left( x^2+4x+4\right) = 3x^3+12x^2+12x $$ |
| ③ | Combine like terms: $$ \color{blue}{3x^3} + \color{red}{12x^2} + \color{green}{12x} + \color{blue}{x^3} + \color{red}{6x^2} + \color{green}{12x} +8 = \color{blue}{4x^3} + \color{red}{18x^2} + \color{green}{24x} +8 $$ |
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