Let's break down the solution step by step.
1. First, we compute the value of the expression [tex]\( 3x^2 - 2y \)[/tex].
- Given [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex], substitute these values into the expression:
[tex]\[
3(3)^2 - 2(5)
\][/tex]
- Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Multiply by 3:
[tex]\[
3 \times 9 = 27
\][/tex]
- Multiply [tex]\( 2 \)[/tex] by [tex]\( 5 \)[/tex]:
[tex]\[
2 \times 5 = 10
\][/tex]
- Subtract the results:
[tex]\[
27 - 10 = 17
\][/tex]
Thus, the value of the expression [tex]\( 3x^2 - 2y \)[/tex] is 17.
2. Next, we compute the value of the expression [tex]\( 2x^2 - 3y \)[/tex].
- Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex] into the expression:
[tex]\[
2(3)^2 - 3(5)
\][/tex]
- Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Multiply by 2:
[tex]\[
2 \times 9 = 18
\][/tex]
- Multiply [tex]\( 3 \)[/tex] by [tex]\( 5 \)[/tex]:
[tex]\[
3 \times 5 = 15
\][/tex]
- Subtract the results:
[tex]\[
18 - 15 = 3
\][/tex]
Thus, the value of the expression [tex]\( 2x^2 - 3y \)[/tex] is 3.
3. Now, we find by how much the value of [tex]\( 3x^2 - 2y \)[/tex] exceeds the value of [tex]\( 2x^2 - 3y \)[/tex].
- Subtract the value of the second expression from the value of the first expression:
[tex]\[
17 - 3 = 14
\][/tex]
Therefore, the value of [tex]\( 3x^2 - 2y \)[/tex] exceeds the value of [tex]\( 2x^2 - 3y \)[/tex] by 14. The answer is [tex]\( \boxed{14} \)[/tex].
