Question
Answer
$$(x+h)^3-x^3=h^3+3h^2x+3hx^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+h)^3-x^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3+3hx^2+3h^2x+h^3-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{x^3}+3hx^2+3h^2x+h^3 -\cancel{x^3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}h^3+3h^2x+3hx^2\end{aligned} $$ | |
| 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 $. $$ \left(x+h\right)^3 = x^3+3 \cdot x^2 \cdot h + 3 \cdot x \cdot h^2+h^3 = x^3+3hx^2+3h^2x+h^3 $$ |
| ② | Combine like terms: $$ \, \color{blue}{ \cancel{x^3}} \,+3hx^2+3h^2x+h^3 \, \color{blue}{ -\cancel{x^3}} \, = h^3+3h^2x+3hx^2 $$ |
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