To solve the expression [tex]\( 3xy(x^2 - xy + y^2) \)[/tex] with [tex]\( x = 1 \)[/tex] and [tex]\( y = -1 \)[/tex], let's break it down into detailed steps:
1. Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -1 \)[/tex] into the expression:
[tex]\( 3 \cdot 1 \cdot (-1) \left(1^2 - 1 \cdot (-1) + (-1)^2\right) \)[/tex]
2. Simplify inside the parentheses first:
- Calculate [tex]\( x^2 \)[/tex]:
[tex]\[
1^2 = 1
\][/tex]
- Calculate [tex]\( xy \)[/tex]:
[tex]\[
1 \cdot (-1) = -1
\][/tex]
- Calculate [tex]\( y^2 \)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
Substitute these values back into the parentheses:
[tex]\[
1 - (-1) + 1
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
1 + 1 + 1 = 3
\][/tex]
4. Substitute back and simplify the overall expression:
[tex]\[
3 \cdot 1 \cdot (-1) \cdot 3
\][/tex]
5. Further simplify the expression:
- First multiply [tex]\( 3 \cdot 1 \)[/tex]:
[tex]\[
3
\][/tex]
- Then multiply [tex]\( 3 \cdot (-1) \)[/tex]:
[tex]\[
-3
\][/tex]
- Finally, multiply [tex]\( -3 \cdot 3 \)[/tex]:
[tex]\[
-9
\][/tex]
So, the value of the expression [tex]\( 3xy(x^2 - xy + y^2) \)[/tex] when [tex]\( x = 1 \)[/tex] and [tex]\( y = -1 \)[/tex] is [tex]\( \boxed{-9} \)[/tex].
