Which expression is equivalent to 3xy − 2xz + yz + 2xy − 4xz − 5yz?
Adding like terms, we have:
(3xy + 2xy) + (-2xz - 4xz) + (yz - 5yz)
Simplifying each set of parentheses, we have:
5xy - 6xz - 4yz
Thus, the expression 5xy - 6xz - 4yz is equivalent to 3xy - 2xz + yz + 2xy - 4xz - 5yz.
To simplify the expression 3xy - 2xz + yz + 2xy - 4xz - 5yz, we can combine like terms.
First, let's group the terms that have the same variables together:
(3xy + 2xy) - (2xz + 4xz) + (yz - 5yz)
Combine the like terms within each group:
5xy - 6xz - 4yz
So the equivalent expression is 5xy - 6xz - 4yz.
To simplify the given expression, we can combine like terms. Like terms are terms that have the same variables raised to the same powers.
Given expression: 3xy - 2xz + yz + 2xy - 4xz - 5yz
To combine like terms, we need to group the terms with the same variables together. Let's group the terms with 'xy', 'xz', and 'yz' variables:
Grouping terms with 'xy': 3xy + 2xy = (3 + 2)xy = 5xy
Grouping terms with 'xz': -2xz - 4xz = (-2 - 4)xz = -6xz
Grouping terms with 'yz': yz - 5yz = (1 - 5)yz = -4yz
Now, we can rewrite the given expression after combining the like terms:
5xy - 6xz - 4yz
So, the expression 5xy - 6xz - 4yz is equivalent to the given expression.