Question
Answer
$$2(x+h)(x+h)(x+h)=2h^3+6h^2x+6hx^2+2x^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x+h)(x+h)(x+h)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x+2h)(x+h)(x+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2+2hx+2hx+2h^2)(x+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(2h^2+4hx+2x^2)(x+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2h^2x+2h^3+4hx^2+4h^2x+2x^3+2hx^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2h^3+6h^2x+6hx^2+2x^3\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( x+h\right) $ $$ \color{blue}{2} \cdot \left( x+h\right) = 2x+2h $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x+2h}\right) $ by each term in $ \left( x+h\right) $. $$ \left( \color{blue}{2x+2h}\right) \cdot \left( x+h\right) = 2x^2+2hx+2hx+2h^2 $$ |
| ③ | Combine like terms: $$ 2x^2+ \color{blue}{2hx} + \color{blue}{2hx} +2h^2 = 2h^2+ \color{blue}{4hx} +2x^2 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{2h^2+4hx+2x^2}\right) $ by each term in $ \left( x+h\right) $. $$ \left( \color{blue}{2h^2+4hx+2x^2}\right) \cdot \left( x+h\right) = 2h^2x+2h^3+4hx^2+4h^2x+2x^3+2hx^2 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{2h^2x} +2h^3+ \color{red}{4hx^2} + \color{blue}{4h^2x} +2x^3+ \color{red}{2hx^2} = 2h^3+ \color{blue}{6h^2x} + \color{red}{6hx^2} +2x^3 $$ |
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