Question

(5x^2y-xy^2)-2(3x^2y+4xy)+2(-5xy+6xy^2)

Answer 1

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.

1. **Distribute the \(-2\)** into the term \(2(3x^2y + 4xy)\):
\[
-2(3x^2y + 4xy) = -6x^2y - 8xy
\]

2. **Distribute the \(2\)** into the term \(2(-5xy + 6xy^2)\):
\[
2(-5xy + 6xy^2) = -10xy + 12xy^2
\]

3. **Now substitute back into the expression**:
\[
(5x^2y - xy^2) - (6x^2y + 8xy) + (-10xy + 12xy^2)
\]

4. **Combine all the terms**:
\[
= 5x^2y - xy^2 - 6x^2y - 8xy - 10xy + 12xy^2
\]

5. **Group like terms together**:
- For \(x^2y\): \(5x^2y - 6x^2y = -x^2y\)
- For \(xy\): \(-8xy - 10xy = -18xy\)
- For \(y^2\): \(-xy^2 + 12xy^2 = 11xy^2\)

6. **Putting it all together**:
\[
-x^2y - 18xy + 11xy^2
\]

Thus, the simplified form of the expression is:
\[
-x^2y - 18xy + 11xy^2
\]