Simplify the polynomial below in stanard form

(2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To simplify the polynomial \((2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)\), we first distribute the negative sign across the second set of parentheses:

\[
(2x^3 - 7x^2 + 4x) - 9x + 5x^3 - 9x^2
\]

Next, we can combine like terms. We will group the terms by their degree:

1. **Cubic terms:**
\[
2x^3 + 5x^3 = 7x^3
\]

2. **Quadratic terms:**
\[
-7x^2 - 9x^2 = -16x^2
\]

3. **Linear terms:**
\[
4x - 9x = -5x
\]

Now we can combine all these results to get the simplified polynomial:

\[
7x^3 - 16x^2 - 5x
\]

Thus, the polynomial in standard form is:

\[
\boxed{7x^3 - 16x^2 - 5x}
\]