To subtract the given polynomials, we need to follow these steps:
1. Write down the expressions clearly:
[tex]\[
4a^3 - 3a - 8
\][/tex]
and
[tex]\[
a - 5
\][/tex]
2. Subtract the second polynomial from the first. When subtracting, distribute the negative sign through the second polynomial:
[tex]\[
(4a^3 - 3a - 8) - (a - 5)
\][/tex]
[tex]\[
= 4a^3 - 3a - 8 - a + 5
\][/tex]
3. Combine like terms:
- The [tex]\(a^3\)[/tex] term remains [tex]\(4a^3\)[/tex] since there are no other [tex]\(a^3\)[/tex] terms to combine.
- Combine the [tex]\(a\)[/tex] terms: [tex]\(-3a - a = -4a\)[/tex].
- Combine the constant terms: [tex]\(-8 + 5 = -3\)[/tex].
4. Write the resulting polynomial in standard form:
[tex]\[
4a^3 - 4a - 3
\][/tex]
Thus, the result of the subtraction in standard form is:
[tex]\[
4a^3 - 4a - 3
\][/tex]
