To find the result of the expression [tex]\((3x + 7y + 4z) - (7x - 5y + 2z)\)[/tex], follow these steps:
1. Distribute the negative sign through the second set of parentheses:
[tex]\[
(3x + 7y + 4z) - (7x - 5y + 2z) = 3x + 7y + 4z - 7x + 5y - 2z
\][/tex]
2. Combine like terms (terms with the same variable):
- For the [tex]\(x\)[/tex] terms: [tex]\(3x - 7x\)[/tex]
- For the [tex]\(y\)[/tex] terms: [tex]\(7y + 5y\)[/tex]
- For the [tex]\(z\)[/tex] terms: [tex]\(4z - 2z\)[/tex]
3. Perform the arithmetic:
- [tex]\(3x - 7x = -4x\)[/tex]
- [tex]\(7y + 5y = 12y\)[/tex]
- [tex]\(4z - 2z = 2z\)[/tex]
4. Write the final result combining the simplified terms:
[tex]\[
-4x + 12y + 2z
\][/tex]
Therefore, the result of [tex]\((3x + 7y + 4z) - (7x - 5y + 2z)\)[/tex] is [tex]\((-4x + 12y + 2z)\)[/tex].
