To simplify the given expression, combine like terms: 3xyz, 7zyx, and 3yzx are combined to get 13xyz; -3xz and 8zx are combined to get 5xz. The simplified expression is e = 13xyz + 5xz + 7yx.
The expression to be simplified is e = 3xyz - 3xz + 7yx + 3yzx + 8zx + 7zyx. First, identify like terms, which are terms that contain the same variables raised to the same powers. In this expression, 3xyz and 7zyx are like terms, as well as 3yzx and 3xyz. Additionally, the terms -3xz and 8zx are like terms because the variable parts only consist of x and z.
Combine the like terms:
- 3xyz + 7zyx + 3yzx = (3+7+3)xyz = 13xyz
- -3xz + 8zx = (8-3)xz = 5xz
The term 7yx has no like terms, so it remains unchanged.
The simplified expression is therefore e = 13xyz + 5xz + 7yx.
After simplifying, always check if the answer is reasonable by ensuring that all like terms have been combined and that no terms have been omitted or altered incorrectly.