simplify 3x 2 2

Daniel Parker

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25-02-2025

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This article explains how to simplify the algebraic expression 3x² + 2x + 2. This expression is already in its simplest form. We'll explore why this is the case and discuss the concept of simplification in algebra.

Understanding Simplification in Algebra

Simplifying an algebraic expression means rewriting it in its most compact and efficient form without changing its value. This usually involves combining like terms and applying the order of operations (PEMDAS/BODMAS).

Like terms are terms that have the same variables raised to the same powers. For example, 3x² and -5x² are like terms, but 3x² and 2x are not.

The order of operations dictates the sequence in which operations should be performed: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Why 3x² + 2x + 2 is Already Simplified

The expression 3x² + 2x + 2 contains three terms: 3x², 2x, and 2. None of these terms are like terms. They have different variables raised to different powers.

• 3x²: This term contains x squared.
• 2x: This term contains x to the power of 1.
• 2: This is a constant term; it doesn't contain any variables.

Because there are no like terms to combine, the expression is already in its simplest form. No further simplification is possible without additional information or context.

Illustrative Examples: When Simplification Is Possible

Let's look at examples where simplification is possible to highlight the contrast:

Example 1:

5x + 2x + 7

Here, 5x and 2x are like terms. We can combine them:

5x + 2x + 7 = 7x + 7

Example 2:

4x² - x² + 3x + 1

Here, 4x² and -x² are like terms. We can combine them:

4x² - x² + 3x + 1 = 3x² + 3x + 1

Conclusion: The Simplicity of 3x² + 2x + 2

In conclusion, the algebraic expression 3x² + 2x + 2 is already in its simplest form. Because it contains no like terms, no further simplification is possible using standard algebraic techniques. Understanding the concept of like terms and the order of operations is crucial for simplifying algebraic expressions. Remember, simplification aims to make expressions more concise and manageable while preserving their mathematical value.