(-2y^{-2}+\frac{3}{2}*y^4)^2+6y^2
You asked:
Evaluate the expression: \({\left( -\left( 2 \cdot {y}^{-2} \right) + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + 6 \cdot {y}^{2}\)
MathBot Answer:
Evaluated
\(\displaystyle {\left( -\left( 2 \cdot {y}^{-2} \right) + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + 6 \cdot {y}^{2} = 6 y^{2} + \left(\frac{3 y^{4}}{2} - \frac{2}{y^{2}}\right)^{2} \)
Expanded
\[{\left( -\left( 2 \cdot {y}^{-2} \right) + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + 6 \cdot {y}^{2} = \frac{9 y^{8}}{4} + \frac{4}{y^{4}}\]
Factored
\[{\left( -\left( 2 \cdot {y}^{-2} \right) + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + 6 \cdot {y}^{2} = \frac{9 y^{12} + 16}{4 y^{4}}\]