https://file.aiquickdraw.com/mathbot/file/1729262767554e3o5wwhc.jpg

Let's analyze and simplify the expressions from the image:

**Expression 3:**  
\[ 3x^3 - x^2 + x \]

This expression is already in its simplest form and can't be factored further using standard factoring techniques. It's a cubic polynomial with terms \( 3x^3 \), \( -x^2 \), and \( +x \).

**Expression 4:**  
\[ 2ax^2 + 2axy - 3bxy - 3bx^2 \]

Here we can simplify by grouping like terms:

1. Group the terms with \( x^2 \) and \( xy \) together:
   \[
   (2ax^2 - 3bx^2) + (2axy - 3bxy)
   \]

2. Factor out common terms:
   \[
   x^2(2a - 3b) + xy(2a - 3b)
   \]

3. Notice that both terms have a common factor of \( (2a - 3b) \), so we can factor it out:
   \[
   (2a - 3b)(x^2 + xy)
   \]

Thus, the factored form of expression 4 is:
\[
(2a - 3b)(x^2 + xy)
\]

Would you like further details on these steps or have any questions?

Here are 5 questions for further exploration:
1. How can we determine whether a cubic polynomial can be factored?
2. What are the conditions for grouping terms in polynomials?
3. Can this approach be used for higher-degree polynomials as well?
4. What is the significance of factoring in solving algebraic equations?
5. How does factoring help in graphing polynomial functions?

**Tip:** When factoring, always look for common terms or patterns such as difference of squares or perfect square trinomials to simplify expressions efficiently.

Simplify and factor the expressions 3x^3 - x^2 + x and 2ax^2 + 2axy - 3bxy - 3bx^2.

Learn how to simplify and factor the polynomial expressions 3x^3 - x^2 + x and 2ax^2 + 2axy - 3bxy - 3bx^2. This lesson explores key algebraic concepts such as factoring by grouping and identifying common factors, suitable for Grades 9-12.

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