\left( -2 \cdot y^{-2} + \frac{3}{2} \cdot y^4 \right) ^2 + \sqrt{36 \cdot y^4}
You asked:
Evaluate the expression: \({\left( -2 \cdot {y}^{-2} + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + \sqrt{36 \cdot {y}^{4}}\)
MathBot Answer:
Evaluated
\(\displaystyle {\left( -2 \cdot {y}^{-2} + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + \sqrt{36 \cdot {y}^{4}} = \left(\frac{3 y^{4}}{2} - \frac{2}{y^{2}}\right)^{2} + 6 \sqrt{y^{4}} \)
Expanded
\[{\left( -2 \cdot {y}^{-2} + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + \sqrt{36 \cdot {y}^{4}} = \frac{9 y^{8}}{4} - 6 y^{2} + 6 \sqrt{y^{4}} + \frac{4}{y^{4}}\]
Factored
\[{\left( -2 \cdot {y}^{-2} + \frac{3}{2} \cdot {y}^{4} \right)}^{2} + \sqrt{36 \cdot {y}^{4}} = \frac{9 y^{12} - 24 y^{6} + 24 y^{4} \sqrt{y^{4}} + 16}{4 y^{4}}\]