(2*n-1)^2 + (2*n+1)^2
You asked:
Evaluate the expression: \({\left( 2 n - 1 \right)}^{2} + {\left( 2 n + 1 \right)}^{2}\)
MathBot Answer:
Evaluated
\(\displaystyle {\left( 2 n - 1 \right)}^{2} + {\left( 2 n + 1 \right)}^{2} = \left(2 n - 1\right)^{2} + \left(2 n + 1\right)^{2} \)
Expanded
\[{\left( 2 n - 1 \right)}^{2} + {\left( 2 n + 1 \right)}^{2} = 8 n^{2} + 2\]
Factored
\[{\left( 2 n - 1 \right)}^{2} + {\left( 2 n + 1 \right)}^{2} = 2 \cdot \left(4 n^{2} + 1\right)\]