Answer
$$(k+2)^3+3k^2+3k+1=k^3+9k^2+15k+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(k+2)^3+3k^2+3k+1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}k^3+6k^2+12k+8+3k^2+3k+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}k^3+9k^2+15k+9\end{aligned} $$ | |
| ① | Find $ \left(k+2\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = k $ and $ B = 2 $. $$ \left(k+2\right)^3 = k^3+3 \cdot k^2 \cdot 2 + 3 \cdot k \cdot 2^2+2^3 = k^3+6k^2+12k+8 $$ |
| ② | Combine like terms: $$ k^3+ \color{blue}{6k^2} + \color{red}{12k} + \color{green}{8} + \color{blue}{3k^2} + \color{red}{3k} + \color{green}{1} = k^3+ \color{blue}{9k^2} + \color{red}{15k} + \color{green}{9} $$ |
This page was created using
Simplify polynomials calculator