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