Certainly! Let's solve the expression [tex]\(2x^2 - 3xy + 3y^2\)[/tex] for [tex]\(x = 6\)[/tex] and [tex]\(y = -5\)[/tex].
Given:
[tex]\[ x = 6 \][/tex]
[tex]\[ y = -5 \][/tex]
We substitute these values into the expression:
[tex]\[ 2x^2 - 3xy + 3y^2 \][/tex]
Step-by-step evaluation:
1. Calculate [tex]\( x^2 \)[/tex]:
[tex]\[ x^2 = 6^2 = 36 \][/tex]
2. Calculate [tex]\( y^2 \)[/tex]:
[tex]\[ y^2 = (-5)^2 = 25 \][/tex]
3. Plug [tex]\( x^2 \)[/tex] into the first term:
[tex]\[ 2x^2 = 2 \times 36 = 72 \][/tex]
4. Calculate [tex]\( xy \)[/tex]:
[tex]\[ xy = 6 \times (-5) = -30 \][/tex]
5. Plug [tex]\( xy \)[/tex] into the second term and consider the coefficient:
[tex]\[ -3xy = -3 \times (-30) = 90 \][/tex]
6. Plug [tex]\( y^2 \)[/tex] into the third term and consider the coefficient:
[tex]\[ 3y^2 = 3 \times 25 = 75 \][/tex]
Now, add these results together:
[tex]\[ 2x^2 - 3xy + 3y^2 = 72 + 90 + 75 = 237 \][/tex]
Therefore, the value of the expression [tex]\( 2x^2 - 3xy + 3y^2 \)[/tex] for [tex]\( x = 6 \)[/tex] and [tex]\( y = -5 \)[/tex] is:
[tex]\[ \boxed{237} \][/tex]
