Math Problem Statement

Simplifying algebraic expressions by combining like terms.

Solution

It appears that the image you've uploaded contains a worksheet about simplifying algebraic expressions by combining like terms. I'll extract and explain the key elements from the image for you:

Key Concepts from the Worksheet:

  1. Terms:

    • Definition: Quantities that you add together to form an algebraic expression are called terms.
    • Example: The expression 4n + 6b - 8 consists of three terms: 4n4n, 6b6b, and 8-8.
  2. Like Terms:

    • Definition: Terms with the same variable raised to the same power.
    • Properties: You can add or subtract like terms.
    • Example of Combining: If you have 5n+3n5n + 3n, you can combine them to get 8n8n, since both terms involve nn.
  3. Combining Like Terms:

    • You can combine terms using addition and subtraction, following the addition rules (commutative and associative).
    • Example: In the expression 5n+3n5n + 3n, combine the nn-terms to get 8n8n.
  4. Unlike Terms:

    • Definition: Terms whose variables are not the same or are raised to different powers.
    • Properties: You cannot add or subtract unlike terms.
    • Example: You cannot combine 4n4n and 6b6b because they have different variables.

Would you like further details on any of these points or some related examples? Here are five related questions you could explore next:

  1. How do you simplify an expression like 3x+4y+5x3x + 4y + 5x?
  2. What are the rules for combining like terms with exponents?
  3. How do you deal with negative signs when combining terms?
  4. Can terms like 3x23x^2 and 5x5x be combined? Why or why not?
  5. How do distributive property and like terms interact in simplifying expressions?

Tip: Always group like terms first before simplifying any algebraic expression to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Algebra
Like terms
Combining like terms
Simplifying expressions

Formulas

Expression with like terms: 4n + 6n = 10n
Expression with unlike terms: 4n + 6b (cannot be combined)

Theorems

Addition and subtraction of like terms
Distributive property

Suitable Grade Level

Grades 6-8