Which expression is equivalent to `\left(3xy\ -\ 2xz\ +\ yz\right)\ +\ \left(2xy\ -\ 4xz\ -\ 5yz\right)?`
The expression `(\left(3xy\ -\ 2xz\ +\ yz\right)\ +\ \left(2xy\ -\ 4xz\ -\ 5yz\right)` can be simplified by combining like terms:
= `(3xy - 2xz + yz) + (2xy - 4xz - 5yz)`
= `3xy - 2xz + yz + 2xy - 4xz - 5yz`
We can group like terms together:
= `(3xy + 2xy) + (-2xz - 4xz) + (yz - 5yz)`
= `5xy - 6xz - 4yz`
Therefore, the equivalent expression is `5xy - 6xz - 4yz`.
Which expression is equivalent to `5x^{2}+3x-2x^{2}+4x?`
To simplify the expression `5x^{2}+3x-2x^{2}+4x`, we can combine like terms.
Grouping the terms with like powers of x:
= `(5x^{2} - 2x^{2}) + (3x + 4x)`
= `3x^{2} + 7x`
Therefore, the equivalent expression is `3x^{2} + 7x`.
Which expression is equivalent to `-3\left(2x+5\right)\ +\ 7\ ?`
To simplify the expression `-3\left(2x+5\right)\ +\ 7`, we need to apply the distributive property by multiplying `-3` to each term inside the parentheses.
= `-3 * 2x - 3 * 5 + 7`
= `-6x - 15 + 7`
= `-6x - 8`
Therefore, the equivalent expression is `-6x - 8`.
To simplify the given expression, you need to combine like terms. Here's how you can do it step-by-step:
Step 1: Remove the parentheses.
\left(3xy\ -\ 2xz\ +\ yz\right)\ +\ \left(2xy\ -\ 4xz\ -\ 5yz\right)
= 3xy - 2xz + yz + 2xy - 4xz - 5yz
Step 2: Combine like terms.
Since the terms have the same variables raised to the same powers, you can combine them.
(3xy + 2xy) + (-2xz - 4xz) + (yz - 5yz)
= 5xy - 6xz - 4yz
Therefore, the expression is equivalent to 5xy - 6xz - 4yz.
To find the expression that is equivalent to `\left(3xy\ -\ 2xz\ +\ yz\right)\ +\ \left(2xy\ -\ 4xz\ -\ 5yz\right)`, you can simply combine like terms by adding or subtracting the coefficients of the same variables.
First, let's add the like terms together:
The terms with `xy` are `3xy` and `2xy`. Adding them gives `3xy + 2xy = 5xy`.
The terms with `xz` are `-2xz` and `-4xz`. Adding them gives `-2xz + (-4xz) = -6xz`.
The terms with `yz` are `yz` and `-5yz`. Adding them gives `yz + (-5yz) = -4yz`.
Now we can combine the simplified terms to get the final expression:
`\left(3xy\ -\ 2xz\ +\ yz\right)\ +\ \left(2xy\ -\ 4xz\ -\ 5yz\right) = 5xy - 6xz - 4yz`.