Answer :
Certainly! Let's find the value of the expression [tex]\(3m^2 + 2p^2 - 15\)[/tex] given [tex]\(m = 3\)[/tex] and [tex]\(p = 10\)[/tex].
### Step-by-Step Solution
1. Substitute the values of [tex]\(m\)[/tex] and [tex]\(p\)[/tex] into the expression:
The given expression is:
[tex]\[ 3m^2 + 2p^2 - 15 \][/tex]
We are given [tex]\(m = 3\)[/tex] and [tex]\(p = 10\)[/tex].
2. Calculate [tex]\(3m^2\)[/tex]:
[tex]\[ m = 3 \Rightarrow 3m^2 = 3 \times (3)^2 = 3 \times 9 = 27 \][/tex]
3. Calculate [tex]\(2p^2\)[/tex]:
[tex]\[ p = 10 \Rightarrow 2p^2 = 2 \times (10)^2 = 2 \times 100 = 200 \][/tex]
4. Add the values of [tex]\(3m^2\)[/tex] and [tex]\(2p^2\)[/tex]:
[tex]\[ 3m^2 + 2p^2 = 27 + 200 = 227 \][/tex]
5. Subtract 15 from the sum:
[tex]\[ 3m^2 + 2p^2 - 15 = 227 - 15 = 212 \][/tex]
### Final Answer
Thus, the value of the expression [tex]\(3m^2 + 2p^2 - 15\)[/tex] when [tex]\(m = 3\)[/tex] and [tex]\(p = 10\)[/tex] is:
[tex]\[ \boxed{212} \][/tex]
Here are the intermediate calculations:
- [tex]\(3m^2 = 27\)[/tex]
- [tex]\(2p^2 = 200\)[/tex]
- [tex]\(3m^2 + 2p^2 - 15 = 212\)[/tex]
So, the final value of the expression is [tex]\(212\)[/tex].
### Step-by-Step Solution
1. Substitute the values of [tex]\(m\)[/tex] and [tex]\(p\)[/tex] into the expression:
The given expression is:
[tex]\[ 3m^2 + 2p^2 - 15 \][/tex]
We are given [tex]\(m = 3\)[/tex] and [tex]\(p = 10\)[/tex].
2. Calculate [tex]\(3m^2\)[/tex]:
[tex]\[ m = 3 \Rightarrow 3m^2 = 3 \times (3)^2 = 3 \times 9 = 27 \][/tex]
3. Calculate [tex]\(2p^2\)[/tex]:
[tex]\[ p = 10 \Rightarrow 2p^2 = 2 \times (10)^2 = 2 \times 100 = 200 \][/tex]
4. Add the values of [tex]\(3m^2\)[/tex] and [tex]\(2p^2\)[/tex]:
[tex]\[ 3m^2 + 2p^2 = 27 + 200 = 227 \][/tex]
5. Subtract 15 from the sum:
[tex]\[ 3m^2 + 2p^2 - 15 = 227 - 15 = 212 \][/tex]
### Final Answer
Thus, the value of the expression [tex]\(3m^2 + 2p^2 - 15\)[/tex] when [tex]\(m = 3\)[/tex] and [tex]\(p = 10\)[/tex] is:
[tex]\[ \boxed{212} \][/tex]
Here are the intermediate calculations:
- [tex]\(3m^2 = 27\)[/tex]
- [tex]\(2p^2 = 200\)[/tex]
- [tex]\(3m^2 + 2p^2 - 15 = 212\)[/tex]
So, the final value of the expression is [tex]\(212\)[/tex].
