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