Answer
$$(x+1)^3-k=x^3+3x^2-k+3x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)^3-k& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3+3x^2+3x+1-k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3+3x^2-k+3x+1\end{aligned} $$ | |
| ① | Find $ \left(x+1\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = x $ and $ B = 1 $. $$ \left(x+1\right)^3 = x^3+3 \cdot x^2 \cdot 1 + 3 \cdot x \cdot 1^2+1^3 = x^3+3x^2+3x+1 $$ |
| ② | Combine like terms: $$ x^3+3x^2-k+3x+1 = x^3+3x^2-k+3x+1 $$ |
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