Which expression is equivalent to `\left(3xy\ -\ 2xz\ +\ yz\right)\ +\ \left(2xy\ -\ 4xz\ -\ 5yz\right)?` i luv dihh

1 answer

To simplify the expression \(\left(3xy - 2xz + yz\right) + \left(2xy - 4xz - 5yz\right)\), we can combine like terms.

  1. Start by writing out the expression: \[ 3xy - 2xz + yz + 2xy - 4xz - 5yz \]

  2. Next, group the like terms together:

    • \(xy\) terms: \(3xy + 2xy\)
    • \(xz\) terms: \(-2xz - 4xz\)
    • \(yz\) terms: \(yz - 5yz\)
  3. Now, perform the addition for each group:

    • For the \(xy\) terms: \[ 3xy + 2xy = 5xy \]
    • For the \(xz\) terms: \[ -2xz - 4xz = -6xz \]
    • For the \(yz\) terms: \[ yz - 5yz = -4yz \]
  4. Combining all these results, we obtain: \[ 5xy - 6xz - 4yz \]

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