n $\sqrt{n}$ + (n+2)$\sqrt{n+1}$
You asked:
Evaluate the expression: \(n \cdot \sqrt{n} + \left(n + 2\right) \cdot \sqrt{n + 1}\)
MathBot Answer:
Evaluated
\(\displaystyle n \cdot \sqrt{n} + \left(n + 2\right) \cdot \sqrt{n + 1} = n^{\frac{3}{2}} + \sqrt{n + 1} \left(n + 2\right) \)
Expanded
\[n \cdot \sqrt{n} + \left(n + 2\right) \cdot \sqrt{n + 1} = n^{\frac{3}{2}} + n \sqrt{n + 1} + 2 \sqrt{n + 1}\]
Factored
\[n \cdot \sqrt{n} + \left(n + 2\right) \cdot \sqrt{n + 1} = n^{\frac{3}{2}} + n \sqrt{n + 1} + 2 \sqrt{n + 1}\]