describe how you would simplify the given expression.

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30-03-2025

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Simplifying algebraic expressions is a fundamental skill in algebra. It involves combining like terms and applying the order of operations to reduce a complex expression to a more manageable form. This article will guide you through the process, providing clear examples and steps to master this important concept. We'll explore simplifying expressions with variables, exponents, and parentheses.

Understanding Like Terms

Before we begin simplifying, it's crucial to understand what "like terms" are. Like terms are terms that have the same variables raised to the same powers. For example:

• 3x and 5x are like terms because they both have the variable x raised to the power of 1.
• 2y² and -7y² are like terms because they both have the variable y raised to the power of 2.
• 4ab and -2ba are like terms because they have the same variables a and b, even if the order is different. (Remember, ab = ba)
• 3x and 3x² are not like terms; the exponents are different.
• 3x and 3y are not like terms; the variables are different.

Step-by-Step Simplification Process

Let's walk through simplifying algebraic expressions step-by-step. We'll use the example: 3x + 2y - 5x + 7y + 4

Step 1: Identify Like Terms

Group the like terms together. In our example:

(3x - 5x) + (2y + 7y) + 4

Step 2: Combine Like Terms

Add or subtract the coefficients (the numbers in front of the variables) of the like terms.

(3 - 5)x + (2 + 7)y + 4

-2x + 9y + 4

Step 3: Write the Simplified Expression

The simplified expression is -2x + 9y + 4. There are no more like terms to combine.

Dealing with Parentheses and Exponents

Simplifying expressions with parentheses or exponents requires following the order of operations (PEMDAS/BODMAS):

• Parentheses/ Brackets
• Exponents/ Orders
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Example with Parentheses:

2(x + 3) - 4x + 5

1. Distribute: Multiply the number outside the parentheses by each term inside. 2(x) + 2(3) - 4x + 5 = 2x + 6 - 4x + 5
2. Combine Like Terms: (2x - 4x) + (6 + 5) = -2x + 11
3. Simplified Expression: -2x + 11

Example with Exponents:

3x² + 5x - 2x² + x

1. Combine Like Terms: (3x² - 2x²) + (5x + x) = x² + 6x
2. Simplified Expression: x² + 6x

More Complex Examples

Let's tackle a more challenging example:

4(2a - b) + 3(a + 2b) - 5a

1. Distribute: 8a - 4b + 3a + 6b - 5a
2. Combine Like Terms: (8a + 3a - 5a) + (-4b + 6b) = 6a + 2b
3. Simplified Expression: 6a + 2b

Practice Makes Perfect

Simplifying algebraic expressions is a skill that improves with practice. The more examples you work through, the more comfortable you'll become with identifying like terms and applying the order of operations. Start with simpler expressions and gradually work your way up to more complex ones. Don't hesitate to consult additional resources and seek help when needed. Mastering this skill is crucial for success in higher-level mathematics.