To simplify the expression \((5x^2y - xy^2) - 2(3x^2y + 4xy) + 2(-5xy + 6xy^2)\), we will distribute and combine like terms step-by-step.
-
Distribute the \(-2\) into the term \(2(3x^2y + 4xy)\): \[ -2(3x^2y + 4xy) = -6x^2y - 8xy \]
-
Distribute the \(2\) into the term \(2(-5xy + 6xy^2)\): \[ 2(-5xy + 6xy^2) = -10xy + 12xy^2 \]
-
Now substitute back into the expression: \[ (5x^2y - xy^2) - (6x^2y + 8xy) + (-10xy + 12xy^2) \]
-
Combine all the terms: \[ = 5x^2y - xy^2 - 6x^2y - 8xy - 10xy + 12xy^2 \]
-
Group like terms together:
- For \(x^2y\): \(5x^2y - 6x^2y = -x^2y\)
- For \(xy\): \(-8xy - 10xy = -18xy\)
- For \(y^2\): \(-xy^2 + 12xy^2 = 11xy^2\)
-
Putting it all together: \[ -x^2y - 18xy + 11xy^2 \]
Thus, the simplified form of the expression is: \[ -x^2y - 18xy + 11xy^2 \]