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