Is (x+1) (3x-2) - 2 in factored form?

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Is (x + 1) (3x-2) -2 in simplified form?

Explain

### Factored Form:

**Definition:** An expression is in **factored form** when it is expressed as a product of its factors, with no additional terms outside the product.

1. The expression \((x + 1)(3x - 2) - 2\) includes a product of two binomials \((x + 1)\) and \((3x - 2)\).
2. However, the expression also includes a subtraction term \(-2\) outside of this product.

**Conclusion:** Since the subtraction \(-2\) is not part of the product, the entire expression is **not in factored form**.

### Simplified Form:

**Definition:** An expression is in **simplified form** when it is fully expanded and all like terms are combined.

1. To determine if \((x + 1)(3x - 2) - 2\) is in simplified form, let's expand it:
   \[
   (x + 1)(3x - 2) = 3x^2 - 2x + 3x - 2 = 3x^2 + x - 2
   \]
   So, the expression becomes:
   \[
   3x^2 + x - 2 - 2 = 3x^2 + x - 4
   \]
2. The expression \(3x^2 + x - 4\) has no like terms to combine further.

**Conclusion:** The expanded form \(3x^2 + x - 4\) is in **simplified form**. Therefore, \((x + 1)(3x - 2) - 2\) is **not in simplified form**.

### Recap:
- The expression \((x + 1)(3x - 2) - 2\) is **not in factored form**.
- The expression \((x + 1)(3x - 2) - 2\) is **not in simplified form**.

Would you like further details or have any questions?

Here are some related questions:
1. How do you factor a quadratic expression?
2. What is the process of expanding binomials?
3. How can you check if an expression is fully simplified?
4. What does it mean for an expression to be in standard form?
5. Can you give examples of expressions in both factored and simplified forms?

**Tip:** When simplifying expressions, always combine like terms and fully expand products before concluding the process.

Is (x+1)(3x-2) - 2 in factored form? Explain. Is (x + 1)(3x-2) - 2 in simplified form? Explain.

Explore whether the expression (x+1)(3x-2) - 2 is in factored or simplified form. This problem delves into key algebraic concepts like factoring and simplifying expressions, making it ideal for students in Grades 8-10.

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