Which expression is equivalent to (3xy-2xz+yz)+(2xy-4xz-5yz)

Answer 1

To simplify the expression \((3xy - 2xz + yz) + (2xy - 4xz - 5yz)\), we start by removing the parentheses and combining like terms.

1. Write out the expression without parentheses: \[ 3xy - 2xz + yz + 2xy - 4xz - 5yz \]

2. Now, group the like terms:

   • The \(xy\) terms: \(3xy + 2xy\)
   • The \(xz\) terms: \(-2xz - 4xz\)
   • The \(yz\) terms: \(yz - 5yz\)

3. Combine each group:

   • For \(xy\): \[ 3xy + 2xy = 5xy \]
   • For \(xz\): \[ -2xz - 4xz = -6xz \]
   • For \(yz\): \[ yz - 5yz = -4yz \]

4. Now, put it all together: \[ 5xy - 6xz - 4yz \]

Thus, the expression equivalent to \((3xy - 2xz + yz) + (2xy - 4xz - 5yz)\) is \[ \boxed{5xy - 6xz - 4yz} \]