Question
Answer
$$(sin(x+c))^3=c^3i^3n^3s^3+3c^2i^3n^3s^3x+3ci^3n^3s^3x^2+i^3n^3s^3x^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(sin(x+c))^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1insx+cins)^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}i^3n^3s^3x^3+3ci^3n^3s^3x^2+3c^2i^3n^3s^3x+c^3i^3n^3s^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}c^3i^3n^3s^3+3c^2i^3n^3s^3x+3ci^3n^3s^3x^2+i^3n^3s^3x^3\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{ins} $ by $ \left( x+c\right) $ $$ \color{blue}{ins} \cdot \left( x+c\right) = insx+cins $$ |
| ② | Find $ \left(insx+cins\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = insx $ and $ B = cins $. $$ \left(insx+cins\right)^3 = \left( insx \right)^3+3 \cdot \left( insx \right)^2 \cdot cins + 3 \cdot insx \cdot \left( cins \right)^2+\left( cins \right)^3 = i^3n^3s^3x^3+3ci^3n^3s^3x^2+3c^2i^3n^3s^3x+c^3i^3n^3s^3 $$ |
| ③ | Combine like terms: $$ c^3i^3n^3s^3+3c^2i^3n^3s^3x+3ci^3n^3s^3x^2+i^3n^3s^3x^3 = c^3i^3n^3s^3+3c^2i^3n^3s^3x+3ci^3n^3s^3x^2+i^3n^3s^3x^3 $$ |
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