Let's evaluate the given expression step by step when [tex]\( a = 2 \)[/tex] and [tex]\( b = 3 \)[/tex].
Given expression:
[tex]\[
3a^2 - 5a - 4(a - b) + 3b
\][/tex]
1. Substitute [tex]\( a = 2 \)[/tex] and [tex]\( b = 3 \)[/tex] into the expression:
[tex]\[
3(2)^2 - 5(2) - 4(2 - 3) + 3(3)
\][/tex]
2. Evaluate the exponentiation and multiplications:
[tex]\[
3(4) - 5(2) - 4(-1) + 3(3)
\][/tex]
3. Simplify each term individually:
[tex]\[
3 \times 4 = 12
\][/tex]
[tex]\[
5 \times 2 = 10
\][/tex]
[tex]\[
4 \times (-1) = -4
\][/tex]
[tex]\[
3 \times 3 = 9
\][/tex]
4. Substitute these values back into the expression:
[tex]\[
12 - 10 - (-4) + 9
\][/tex]
5. Simplify the addition and subtraction sequence:
[tex]\[
12 - 10 + 4 + 9
\][/tex]
[tex]\[
2 + 4 + 9
\][/tex]
[tex]\[
6 + 9
\][/tex]
[tex]\[
15
\][/tex]
Therefore, the value of the expression when [tex]\( a = 2 \)[/tex] and [tex]\( b = 3 \)[/tex] is:
[tex]\[
\boxed{15}
\][/tex]
