Consider the following expression.
\(x + 2 y - 2 z\) - (x - 2 y + 2 z)
(a) Simplify the expression.
4y-4z
first off, I like to circle to common ones... so I first circle the two x's. Since we are subtracting, it would be x-x which is 0. Thenm i circled the 2y's. It would be
2y - (-2Y) aka 2y +2y which is 4y. Then, -2z-2z which is -4z.
it would be 0+4y-4z and you obviously do not need the zero so the guy up there, visoth is right.
To simplify the expression, we need to combine like terms and perform the indicated operations.
Let's start by removing the parentheses in the expression. When subtracting a quantity within parentheses, we need to distribute the negative sign to each term inside the parentheses:
\(x + 2y - 2z - (x - 2y + 2z)\)
Distributing the negative sign inside the parentheses:
\(x + 2y - 2z - x + 2y - 2z\)
Next, we can combine like terms. Like terms are terms that have the same variables raised to the same exponents. In this case, the terms \(x\) and \(-x\) cancel each other out, and the terms \(2y\) and \(2y\) can be combined, as well as the terms \(-2z\) and \(-2z\):
\(x - x + 2y + 2y - 2z - 2z\)
Simplifying further:
\(0 + 4y - 4z\)
Finally, the simplified expression is \(4y - 4z\).