Answer :
We want to simplify the expression
$$
\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right).
$$
**Step 1. Distribute the negative sign**
When subtracting the polynomial inside the parentheses, distribute the negative sign to each term:
$$
\left(5x^3 + 4x^2\right) - 6x^2 + 2x + 9.
$$
**Step 2. Combine like terms**
Now, group and combine like terms:
- The term $5x^3$ has no like term.
- Combine the $x^2$ terms: $4x^2 - 6x^2 = -2x^2$.
- The $x$ term is $2x$, and the constant term is $9$.
So the expression becomes:
$$
5x^3 - 2x^2 + 2x + 9.
$$
Thus, the difference of the polynomials is
$$
\boxed{5x^3 - 2x^2 + 2x + 9}.
$$
$$
\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right).
$$
**Step 1. Distribute the negative sign**
When subtracting the polynomial inside the parentheses, distribute the negative sign to each term:
$$
\left(5x^3 + 4x^2\right) - 6x^2 + 2x + 9.
$$
**Step 2. Combine like terms**
Now, group and combine like terms:
- The term $5x^3$ has no like term.
- Combine the $x^2$ terms: $4x^2 - 6x^2 = -2x^2$.
- The $x$ term is $2x$, and the constant term is $9$.
So the expression becomes:
$$
5x^3 - 2x^2 + 2x + 9.
$$
Thus, the difference of the polynomials is
$$
\boxed{5x^3 - 2x^2 + 2x + 9}.
$$
