X²+2 (3/5 * x⅔-y)² -1
You asked:
Evaluate the expression: \({X}^{2} + 2 {\left( \frac{3}{5} \cdot x\left( \frac{2}{3} \right) - y \right)}^{2} - 1\)
MathBot Answer:
Evaluated
\(\displaystyle {X}^{2} + 2 {\left( \frac{3}{5} \cdot x\left( \frac{2}{3} \right) - y \right)}^{2} - 1 = X^{2} + 2 \left(- y + \frac{3 x{\left(\frac{2}{3} \right)}}{5}\right)^{2} - 1 \)
Expanded
\[{X}^{2} + 2 {\left( \frac{3}{5} \cdot x\left( \frac{2}{3} \right) - y \right)}^{2} - 1 = X^{2} + 2 y^{2} - \frac{12 y x{\left(\frac{2}{3} \right)}}{5} + \frac{18 x^{2}{\left(\frac{2}{3} \right)}}{25} - 1\]
Factored
\[{X}^{2} + 2 {\left( \frac{3}{5} \cdot x\left( \frac{2}{3} \right) - y \right)}^{2} - 1 = \frac{25 X^{2} + 50 y^{2} - 60 y x{\left(\frac{2}{3} \right)} + 18 x^{2}{\left(\frac{2}{3} \right)} - 25}{25}\]