Sure, let's simplify the given expression step by step with the provided values [tex]\( x = 1 \)[/tex], [tex]\( y = 0 \)[/tex], and [tex]\( z = -1 \)[/tex].
The expression to simplify is:
[tex]\[ (2x - y) + y(z - 2) + x(y + z) \][/tex]
### Step-by-Step Solution:
1. Substitute the values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] into the expression:
Given [tex]\( x = 1 \)[/tex], [tex]\( y = 0 \)[/tex], and [tex]\( z = -1 \)[/tex], we substitute these values into the expression:
[tex]\[ (2 \cdot 1 - 0) + 0 \cdot (-1 - 2) + 1 \cdot (0 - 1) \][/tex]
2. Simplify each part of the expression:
- First part: [tex]\( 2x - y \)[/tex]
[tex]\[ 2 \cdot 1 - 0 = 2 \][/tex]
- Second part: [tex]\( y(z - 2) \)[/tex]
[tex]\[ 0 \cdot (-1 - 2) = 0 \][/tex]
- Third part: [tex]\( x(y + z) \)[/tex]
[tex]\[ 1 \cdot (0 - 1) = -1 \][/tex]
3. Combine the simplified parts:
[tex]\[ 2 + 0 + (-1) \][/tex]
4. Simplify the expression further:
[tex]\[ 2 + 0 - 1 = 1 \][/tex]
### Conclusion:
The simplified value of the given expression is:
[tex]\[ 1 \][/tex]
So, the value of the expression [tex]\((2x - y) + y(z - 2) + x(y + z)\)[/tex] when [tex]\( x = 1 \)[/tex], [tex]\( y = 0 \)[/tex], and [tex]\( z = -1 \)[/tex] is [tex]\( 1 \)[/tex].
