(n-1)³+3(n-1)²+2(n-1)

asked by guest
on Oct 25, 2024 at 10:16 am



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

\[{\left( n - 1 \right)}^{3} + 3 \cdot {\left( n - 1 \right)}^{2} + 2 \cdot \left(n - 1\right) = n \left(n - 1\right) \left(n + 1\right)\]

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