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