Sure, let's solve the expression [tex]\( x^2 - 2xy + y^2 \)[/tex] step by step with the given values [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex].
1. Substitute the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the expression:
[tex]\[
x^2 - 2xy + y^2 = 3^2 - 2 \cdot 3 \cdot 2 + 2^2
\][/tex]
2. Calculate each term individually:
- Calculate [tex]\( x^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Calculate [tex]\( -2xy \)[/tex]:
[tex]\[
-2 \cdot 3 \cdot 2 = -12
\][/tex]
- Calculate [tex]\( y^2 \)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
3. Combine these results:
[tex]\[
9 - 12 + 4
\][/tex]
4. Add and subtract the terms in sequence:
[tex]\[
9 - 12 = -3
\][/tex]
[tex]\[
-3 + 4 = 1
\][/tex]
So, 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].
