(xy+3x+2y+6/xy-x+2y)(9x-9y/12) simplify
You asked:
Evaluate the expression: \(\left(x y + 3 x + 2 y + \frac{6}{x y} - x + 2 y\right) \cdot \left(9 x - \frac{9 y}{12}\right)\)
MathBot Answer:
Evaluated
\(\displaystyle \left(x y + 3 x + 2 y + \frac{6}{x y} - x + 2 y\right) \cdot \left(9 x - \frac{9 y}{12}\right) = \left(9 x - \frac{3 y}{4}\right) \left(x y + 2 x + 4 y + \frac{6}{x y}\right) \)
Expanded
\[\left(x y + 3 x + 2 y + \frac{6}{x y} - x + 2 y\right) \cdot \left(9 x - \frac{9 y}{12}\right) = 9 x^{2} y + 18 x^{2} - \frac{3 y^{2} x}{4} + \frac{69 x y}{2} - 3 y^{2} + \frac{54}{y} - \frac{9}{2 x}\]
Factored
\[\left(x y + 3 x + 2 y + \frac{6}{x y} - x + 2 y\right) \cdot \left(9 x - \frac{9 y}{12}\right) = \frac{3 \cdot \left(12 x - y\right) \left(x^{2} y^{2} + 2 x^{2} y + 4 y^{2} x + 6\right)}{4 x y}\]