Let's simplify each given expression step-by-step.
### Expression 2: [tex]\( 4x - (3y - x + 2z) \)[/tex]
1. Distribute the negative sign inside the parentheses:
[tex]\[
4x - 3y + x - 2z
\][/tex]
2. Combine like terms:
[tex]\[
4x + x - 3y - 2z
\][/tex]
3. Simplify:
[tex]\[
5x - 3y - 2z
\][/tex]
### Expression 4: [tex]\(-3(a + b) + 4(2a - 3b) - (2a - b)\)[/tex]
1. Distribute the constants inside each parentheses:
[tex]\[
-3a - 3b + 8a - 12b - 2a + b
\][/tex]
2. Combine like terms:
[tex]\[
(-3a + 8a - 2a) + (-3b - 12b + b)
\][/tex]
3. Simplify:
[tex]\[
3a - 14b
\][/tex]
### Expression 6: [tex]\(-2(x^2 - y^2 + xy) - 3(x^2 + y^2 - xy)\)[/tex]
1. Distribute the constants inside each parentheses:
[tex]\[
-2x^2 + 2y^2 - 2xy - 3x^2 - 3y^2 + 3xy
\][/tex]
2. Combine like terms:
[tex]\[
(-2x^2 - 3x^2) + (2y^2 - 3y^2) + (-2xy + 3xy)
\][/tex]
3. Simplify:
[tex]\[
-5x^2 - y^2 + xy
\][/tex]
### Expression 8: [tex]\(-x + [5y - \{x - (5y - 2x)\}]\)[/tex]
1. Simplify the innermost parentheses:
[tex]\[
5y - \{x - 5y + 2x\}
\][/tex]
2. Remove brackets and combine like terms inside them:
[tex]\[
5y - (3x - 5y)
\][/tex]
3. Distribute the negative sign inside the parentheses:
[tex]\[
5y - 3x + 5y
\][/tex]
4. Combine like terms:
[tex]\[
10y - 3x
\][/tex]
5. Adjust the expression:
[tex]\[
-x + 10y - 3x
\][/tex]
6. Combine like terms:
[tex]\[
-4x + 10y
\][/tex]
So, the final simplified expressions are:
1. [tex]\(5x - 3y - 2z\)[/tex]
2. [tex]\(3a - 14b\)[/tex]
3. [tex]\(-5x^2 + xy - y^2\)[/tex]
4. [tex]\(-4x + 10y\)[/tex]
