A multi-step algebraic expression can be interpreted as a sequence of operations and rewritten in an equivalent, simpler form using order of operations, the distributive property, and combination of like terms. This includes expressions with parentheses, variables, constants, and integer or rational coefficients; terms may be combined only when their variable parts match, supporting later equation solving and polynomial work without extending to formal factoring or advanced polynomial operations.
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Detailed Explanation: Simplify multi-step algebraic expressions
To simplify a multi-step algebraic expression, follow these steps:
- Use the distributive property to remove parentheses.
- Combine like terms—terms with the same variable part.
- Keep unlike terms separate.
Example:
Step 1: Distribute the .
Multiply by each term inside the parentheses:
Step 2: Group like terms.
The variable terms and are like terms. The constants and are also like terms:
Step 3: Combine each group.
Therefore,
Remember: You can combine and because both have the same variable part, . You cannot combine a variable term with a constant.
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Like Terms - Combine - Order N - Whole - Multiple Variables - Expression to Pair
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Download/Modify Free Grade 8 'Simplify multi-step algebraic expressions' Worksheet
Print this free 'Simplify multi-step algebraic expressions' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Like Terms - Combine - Order N - Whole - Multiple Variables - Expression to Pair
- Like Terms - Combine - Order 2 - Whole - Multiple Variables - Expression to Pair
- Like Terms - Combine - Order N - Whole - One Variable - Pair to True or False
- Like Terms - Combine - Order N - Whole - Multiple Variables - Pair to True or False
- Like Terms - Combine - Order 1 - Whole - Multiple Variables - Expression to Pair
- Like Terms - Combine - Order 1 - Fractional - One Variable - Expression to Pair
- Order of Operations - Add, Subtract, Multiply with Parentheses (4 Numbers)
- Order of Operations - Add, Subtract, Multiply no Parentheses (4 Numbers)
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