If `x=2a^(2)+3b^(2)-5ab, y=b^(2)-3a^(2)+7ab and z=6a^(2)-b^(2)+ab`, find:
`x+y-z`

Answer

To solve the problem, we need to find the expression \( x + y - z \) given the values of \( x \), \( y \), and \( z \).

1. **Write down the expressions for \( x \), \( y \), and \( z \)**:
- \( x = 2a^2 + 3b^2 - 5ab \)
- \( y = b^2 - 3a^2 + 7ab \)
- \( z = 6a^2 - b^2 + ab \)

2. **Calculate \( x + y \)**:
\[ x + y = (2a^2 + 3b^2 - 5ab) + (b^2 - 3a^2 + 7ab) \]
Combine like terms:
- Combine \( a^2 \) terms: \( 2a^2 - 3a^2 = -a^2 \)
- Combine \( b^2 \) terms: \( 3b^2 + b^2 = 4b^2 \)
- Combine \( ab \) terms: \( -5ab + 7ab = 2ab \)

So,
\[ x + y = -a^2 + 4b^2 + 2ab \]

3. **Now, subtract \( z \) from \( x + y \)**:
\[ x + y - z = (-a^2 + 4b^2 + 2ab) - (6a^2 - b^2 + ab) \]
Distributing the negative sign:
\[ = -a^2 + 4b^2 + 2ab - 6a^2 + b^2 - ab \]
Combine like terms:
- Combine \( a^2 \) terms: \( -a^2 - 6a^2 = -7a^2 \)
- Combine \( b^2 \) terms: \( 4b^2 + b^2 = 5b^2 \)
- Combine \( ab \) terms: \( 2ab - ab = ab \)

So,
\[ x + y - z = -7a^2 + 5b^2 + ab \]

4. **Final Result**:
\[ x + y - z = -7a^2 + 5b^2 + ab \]