To solve the expression [tex]\(a^4 + a^3 - a^2\)[/tex], we need to evaluate each term step by step for any given value of [tex]\(a\)[/tex]. Here's a detailed breakdown:
1. Calculate [tex]\(a^4\)[/tex] (a raised to the fourth power):
[tex]\[
a^4 = a \times a \times a \times a
\][/tex]
2. Calculate [tex]\(a^3\)[/tex] (a raised to the third power):
[tex]\[
a^3 = a \times a \times a
\][/tex]
3. Calculate [tex]\(a^2\)[/tex] (a raised to the second power):
[tex]\[
a^2 = a \times a
\][/tex]
4. Substitute these values back into the expression:
[tex]\[
a^4 + a^3 - a^2
\][/tex]
### Example Calculation
Let's take an example where [tex]\(a = 2\)[/tex]:
1. Calculate [tex]\(2^4\)[/tex]:
[tex]\[
2^4 = 2 \times 2 \times 2 \times 2 = 16
\][/tex]
2. Calculate [tex]\(2^3\)[/tex]:
[tex]\[
2^3 = 2 \times 2 \times 2 = 8
\][/tex]
3. Calculate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 2 \times 2 = 4
\][/tex]
4. Substitute these values back into the expression:
[tex]\[
a^4 + a^3 - a^2 = 16 + 8 - 4
\][/tex]
5. Simplify the expression:
[tex]\[
16 + 8 - 4 = 20
\][/tex]
So, for [tex]\(a = 2\)[/tex], the value of the expression [tex]\(a^4 + a^3 - a^2\)[/tex] is 20.
### General Solution
For any value of [tex]\(a\)[/tex], you can follow the same steps:
1. Compute [tex]\(a^4\)[/tex].
2. Compute [tex]\(a^3\)[/tex].
3. Compute [tex]\(a^2\)[/tex].
4. Add the results of [tex]\(a^4\)[/tex] and [tex]\(a^3\)[/tex].
5. Subtract [tex]\(a^2\)[/tex] from the result of step 4.
This will give you the value of the expression [tex]\(a^4 + a^3 - a^2\)[/tex] for any input [tex]\(a\)[/tex].
