Of course! Let's evaluate the expression [tex]\(-2p^3 - 3p^2 + 4p + 7\)[/tex] step by step for [tex]\(p = -2\)[/tex].
1. Evaluate [tex]\(p^3\)[/tex]:
- First, we need to find the cube of -2:
[tex]\[
p^3 = (-2)^3 = -8
\][/tex]
2. Calculate [tex]\(-2p^3\)[/tex]:
- Next, we multiply the cube of -2 by -2:
[tex]\[
-2p^3 = -2 \times (-8) = 16
\][/tex]
So, the first term is 16.
3. Evaluate [tex]\(p^2\)[/tex]:
- Now we need to find the square of -2:
[tex]\[
p^2 = (-2)^2 = 4
\][/tex]
4. Calculate [tex]\(-3p^2\)[/tex]:
- Then, we multiply the square of -2 by -3:
[tex]\[
-3p^2 = -3 \times 4 = -12
\][/tex]
So, the second term is -12.
5. Calculate [tex]\(4p\)[/tex]:
- Now we multiply -2 by 4:
[tex]\[
4p = 4 \times (-2) = -8
\][/tex]
So, the third term is -8.
6. Collect the constant term:
- The constant term in the expression is 7. So, our fourth term is 7.
7. Sum all the calculated terms:
Now we need to sum all the terms together:
[tex]\[
16 + (-12) + (-8) + 7
\][/tex]
Let's perform the addition step-by-step:
- First, [tex]\(16 + (-12) = 4\)[/tex]
- Next, [tex]\(4 + (-8) = -4\)[/tex]
- Finally, [tex]\(-4 + 7 = 3\)[/tex]
Therefore, the value of the expression [tex]\(-2p^3 - 3p^2 + 4p + 7\)[/tex] when [tex]\(p = -2\)[/tex] is [tex]\(3\)[/tex].
To summarize:
- First term: [tex]\(16\)[/tex]
- Second term: [tex]\(-12\)[/tex]
- Third term: [tex]\(-8\)[/tex]
- Fourth term: [tex]\(7\)[/tex]
- Final result: [tex]\(3\)[/tex]
