Sure, let's solve the expression step by step:
Given the expression:
[tex]\[ X^3 + 2XYX - Y^2 \][/tex]
We are provided with the values for [tex]\(X\)[/tex], [tex]\(Y\)[/tex], and [tex]\(Z\)[/tex] which are:
[tex]\[ X = 1 \][/tex]
[tex]\[ Y = 1 \][/tex]
[tex]\[ Z = 1 \][/tex]
Let's find the value of each term in the expression:
1. Calculate [tex]\(X^3\)[/tex]:
[tex]\[ X^3 = 1^3 = 1 \][/tex]
2. Calculate [tex]\(2XYX\)[/tex] (we can simplify this to [tex]\(2XYZ\)[/tex]):
[tex]\[ 2 \cdot 1 \cdot 1 \cdot 1 = 2 \][/tex]
3. Calculate [tex]\(Y^2\)[/tex]:
[tex]\[ Y^2 = 1^2 = 1 \][/tex]
Now, substitute these values back into the expression:
[tex]\[ X^3 + 2XYZ - Y^2 \][/tex]
[tex]\[ 1 + 2 - 1 \][/tex]
Finally, combine the terms:
[tex]\[ 1 + 2 - 1 = 2 \][/tex]
So, the value of the expression [tex]\(X^3 + 2XYZ - Y^2\)[/tex] is:
[tex]\[ 2 \][/tex]
