Answer
$$(2+h)^3-3\cdot(2+h)+4=h^3+6h^2+9h+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2+h)^3-3\cdot(2+h)+4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8+12h+6h^2+h^3-3\cdot(2+h)+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8+12h+6h^2+h^3-(6+3h)+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8+12h+6h^2+h^3-6-3h+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}h^3+6h^2+9h+6\end{aligned} $$ | |
| ① | Find $ \left(2+h\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 2 $ and $ B = h $. $$ \left(2+h\right)^3 = 2^3+3 \cdot 2^2 \cdot h + 3 \cdot 2 \cdot h^2+h^3 = 8+12h+6h^2+h^3 $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( 2+h\right) $ $$ \color{blue}{3} \cdot \left( 2+h\right) = 6+3h $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6+3h \right) = -6-3h $$ |
| ④ | Combine like terms: $$ \color{blue}{8} + \color{red}{12h} +6h^2+h^3 \color{green}{-6} \color{red}{-3h} + \color{green}{4} = h^3+6h^2+ \color{red}{9h} + \color{green}{6} $$ |
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