Certainly! To find the value of the expression [tex]\( x^2 - y^2 - z^2 \)[/tex] given the values [tex]\( x = 1 \)[/tex], [tex]\( y = 2 \)[/tex], and [tex]\( z = 3 \)[/tex], follow these steps:
1. Substitute the values into the expression.
[tex]\[
x = 1, \quad y = 2, \quad z = 3
\][/tex]
2. Calculate [tex]\( x^2 \)[/tex]:
[tex]\[
x^2 = 1^2 = 1
\][/tex]
3. Calculate [tex]\( y^2 \)[/tex]:
[tex]\[
y^2 = 2^2 = 4
\][/tex]
4. Calculate [tex]\( z^2 \)[/tex]:
[tex]\[
z^2 = 3^2 = 9
\][/tex]
5. Substitute these values back into the expression [tex]\( x^2 - y^2 - z^2 \)[/tex]:
[tex]\[
x^2 - y^2 - z^2 = 1 - 4 - 9
\][/tex]
6. Perform the subtraction:
[tex]\[
1 - 4 - 9 = -3 - 9 = -12
\][/tex]
Therefore, the value of the expression [tex]\( x^2 - y^2 - z^2 \)[/tex] when [tex]\( x = 1 \)[/tex], [tex]\( y = 2 \)[/tex], and [tex]\( z = 3 \)[/tex] is [tex]\(-12\)[/tex].
