To find the difference between the two expressions [tex]\( x^3 + 1 \)[/tex] and [tex]\( x^2 - 2 \)[/tex], we can follow these steps:
1. Write down the expressions:
[tex]\[
\text{First expression: } x^3 + 1
\][/tex]
[tex]\[
\text{Second expression: } x^2 - 2
\][/tex]
2. Set up the subtraction:
[tex]\[
(x^3 + 1) - (x^2 - 2)
\][/tex]
3. Distribute the subtraction:
[tex]\[
x^3 + 1 - x^2 + 2
\][/tex]
4. Combine like terms:
- [tex]\( x^3 \)[/tex] is the only cubic term.
- [tex]\(- x^2\)[/tex] is the quadratic term.
- [tex]\(1 + 2\)[/tex] are the constant terms which sum up to [tex]\( 3 \)[/tex].
Therefore:
[tex]\[
x^3 - x^2 + 3
\][/tex]
So, the difference in the form [tex]\( x^3 + ax^2 + bx + c \)[/tex] is:
[tex]\[
x^3 - x^2 + 3
\][/tex]
Hence, the completed difference is:
[tex]\[
x^3 + (-1)x^2 + 0x + 3
\][/tex]
