Add 38𝑥 minus 33𝑦 plus 28𝑧, 24𝑦 minus 23𝑥 minus 23𝑧, and 24𝑥 minus 11𝑧 minus 17𝑦 then subtract the result from 26𝑥 minus 17𝑦 plus 19𝑧.
Our first step is to add the three expressions. In order to do this, we’ll group or collect the like terms. We’ll group the 𝑥s, then we’ll group the 𝑦s, then we’ll group the 𝑧s.
Grouping the 𝑥 terms gives us 38𝑥 minus 23𝑥 plus 24𝑥. This is equal to 39𝑥. Next, we’ll group the 𝑦 terms: negative 33𝑦 plus 24𝑦 minus 17𝑦. This is equal to negative 26𝑦 as negative 33 plus 24 minus 17 is equal to negative 26. Finally, we need to group the 𝑧 terms: 28𝑧 minus 23𝑧 minus 11𝑧. This is equal to minus six 𝑧 as 28 minus 23 minus 11 is equal to negative six.
Adding the three expressions 38𝑥 minus 33𝑦 plus 28𝑧, 24𝑦 minus 23𝑥 minus 23𝑧, and 24𝑥 minus 11𝑧 minus 17𝑦 gives us 39𝑥 minus 26𝑦 minus six 𝑧. We were then asked to subtract the result from 26𝑥 minus 17𝑦 plus 19𝑧. This can be written as 26𝑥 minus 17𝑦 plus 19𝑧 minus 39𝑥 minus 26𝑦 minus six 𝑧.
Once again, we need to group the like terms. 26𝑥 minus 39𝑥 is negative 13𝑥 as 26 minus 39 is negative 13. Negative 17𝑦 minus negative 26𝑦 is plus nine 𝑦 as negative 17 minus negative 26 is the same as negative 17 plus 26, which gives us an answer of nine. Finally, 19𝑧 minus negative six 𝑧 is equal to 25𝑧 as 19 minus negative six is equal to 25.
This means that our final answer is negative 13𝑥 plus nine 𝑦 plus 25𝑧.