To solve the expression \( x^2 - 2xy + y^2 \) when \( x = 3 \) and \( y = 2 \), we need to substitute the given values into the expression and simplify step by step.
1. Substitute \( x = 3 \) and \( y = 2 \) into the expression:
[tex]\[
(3)^2 - 2 \cdot (3) \cdot (2) + (2)^2
\][/tex]
2. Calculate \( (3)^2 \):
[tex]\[
(3)^2 = 9
\][/tex]
3. Calculate \( 2 \cdot (3) \cdot (2) \):
[tex]\[
2 \cdot 3 \cdot 2 = 12
\][/tex]
4. Calculate \( (2)^2 \):
[tex]\[
(2)^2 = 4
\][/tex]
5. Substitute these values back into the expression:
[tex]\[
9 - 12 + 4
\][/tex]
6. Perform the subtraction and addition operations:
[tex]\[
9 - 12 = -3
\][/tex]
7. Then,
[tex]\[
-3 + 4 = 1
\][/tex]
Therefore, the result of the expression [tex]\( x^2 - 2xy + y^2 \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex] is [tex]\( 1 \)[/tex].
