solve this operations of functions in subtraction: (3x^4+2x^3=2x^2-3x+2)-(9x^2+x-3)

Let's solve the subtraction of two functions step by step:

Given:
\[
(3x^4 + 2x^3 + 2x^2 - 3x + 2) - (9x^2 + x - 3)
\]

### Step 1: Distribute the negative sign to the second polynomial:
\[
(3x^4 + 2x^3 + 2x^2 - 3x + 2) - 9x^2 - x + 3
\]
This gives:
\[
3x^4 + 2x^3 + 2x^2 - 3x + 2 - 9x^2 - x + 3
\]

### Step 2: Combine like terms:
- \(3x^4\) (no like terms, remains \(3x^4\)),
- \(2x^3\) (no like terms, remains \(2x^3\)),
- \(2x^2 - 9x^2 = -7x^2\),
- \(-3x - x = -4x\),
- \(2 + 3 = 5\).

### Final Answer:
\[
3x^4 + 2x^3 - 7x^2 - 4x + 5
\]

Would you like to go into more detail or have any questions?

Here are 5 related questions for you:
1. How do you add two polynomials?
2. How do you find the degree of a polynomial?
3. What is the process of distributing a negative sign in polynomial subtraction?
4. Can you solve polynomial multiplication, such as \((x^2 + 3x)(x - 1)\)?
5. What is the derivative of the polynomial \(3x^4 + 2x^3 - 7x^2 - 4x + 5\)?

**Tip**: Always group like terms first when subtracting polynomials to avoid errors.

solve this operations of functions in subtraction: (3x^4+2x^3+2x^2-3x+2)-(9x^2+x-3)

Learn how to subtract two polynomials, (3x^4+2x^3+2x^2-3x+2) and (9x^2+x-3), by distributing the negative sign and combining like terms. This detailed guide walks through each step of the solution, covering key algebraic concepts. Suitable for students in Grades 8-10.

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