Let's find the value of the expression [tex]\( z^3 - 5xy + 3xyz \)[/tex] given that [tex]\( x = 1 \)[/tex], [tex]\( y = -1 \)[/tex], and [tex]\( z = -2 \)[/tex].
Step-by-Step Solution:
1. Substitute the values into the expression:
Given:
[tex]\[
x = 1, \quad y = -1, \quad z = -2
\][/tex]
The expression to evaluate is:
[tex]\[
z^3 - 5xy + 3xyz
\][/tex]
2. Calculate each term separately:
First term: [tex]\( z^3 \)[/tex]
[tex]\[
z^3 = (-2)^3 = -8
\][/tex]
Second term: [tex]\( -5xy \)[/tex]
[tex]\[
-5xy = -5 \times 1 \times (-1) = 5
\][/tex]
Third term: [tex]\( 3xyz \)[/tex]
[tex]\[
3xyz = 3 \times 1 \times (-1) \times (-2) = 6
\][/tex]
3. Sum the terms:
Now, we add the calculated terms together:
[tex]\[
z^3 + (-5xy) + 3xyz = -8 + 5 + 6
\][/tex]
4. Compute the total:
[tex]\[
-8 + 5 = -3
\][/tex]
[tex]\[
-3 + 6 = 3
\][/tex]
Therefore, the value of the expression [tex]\( z^3 - 5xy + 3xyz \)[/tex] when [tex]\( x = 1 \)[/tex], [tex]\( y = -1 \)[/tex], and [tex]\( z = -2 \)[/tex] is [tex]\( 3 \)[/tex].
Summary of individual terms:
[tex]\[
z^3 = -8
\][/tex]
[tex]\[
-5xy = 5
\][/tex]
[tex]\[
3xyz = 6
\][/tex]
Final Result:
[tex]\[
z^3 - 5xy + 3xyz = 3
\][/tex]
