Question

mixed review.

1. $(x^5 + 3x - 5x^2 + 2) - (x^2 + 4x^3 + x^5) + (x - 3x^2 + 5)$

Explanation:

Step1: Remove parentheses

First, we remove the parentheses by distributing the negative sign in the second term and the positive sign in the third term.
\[

$$\begin{align*} &(x^5 + 3x - 5x^2 + 2) - (x^2 + 4x^3 + x^5) + (x - 3x^2 + 5)\\ =&x^5 + 3x - 5x^2 + 2 - x^2 - 4x^3 - x^5 + x - 3x^2 + 5 \end{align*}$$

\]

Step2: Combine like terms

Next, we combine the like terms. Let's combine the \(x^5\) terms, the \(x^3\) terms, the \(x^2\) terms, the \(x\) terms, and the constant terms separately.

• For \(x^5\) terms: \(x^5 - x^5 = 0\)
• For \(x^3\) terms: \(-4x^3\) (only one term)
• For \(x^2\) terms: \(-5x^2 - x^2 - 3x^2 = -9x^2\)
• For \(x\) terms: \(3x + x = 4x\)
• For constant terms: \(2 + 5 = 7\)

Putting it all together, we get:
\[
-4x^3 - 9x^2 + 4x + 7
\]

Answer:

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