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Simplifying Algebraic Expressions

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Simplifying Algebraic Expressions

Identify like terms, then simplify by combining coefficients and constants. Show your work for expressions that require more than one step.

Recognize Like Terms

Like terms have the same variable part, including the same exponents. Constants are like terms with one another.

1.In the expression 8x + 5 + 3x + 11, write the two like-term pairs.
2.Which choices show pairs of like terms? Select every correct answer.
  • 4m and 9m
  • 6 and 13
  • 2a and 2b
  • 7p and 7p²
  • 3y² and 8y²
3.What is the coefficient of n in the term −12n?
  • −12
  • 12
  • n
  • −12n
4.Match each term with its variable part or category.
  • −6r
  • 4s²
  • 15
  • −2t³
  • 9r
  • r
  • t³
  • constant
  • r
  • s²

Combine Like Terms

Simplify each expression. Keep unlike variable parts separate.

5.Simplify 7k + 4 − 2k + 9.
6.Simplify 6d + 3e − 2d + 5e.
7.Simplify 9q − 12 + 4q + 7.
8.Simplify 5x² + 3x − 2x² + 8x.

Use the Distributive Property

Multiply the factor outside the parentheses by every term inside, then combine like terms.

9.Simplify 3(2a + 5) − 4a.
10.Simplify 2(4b − 3) + 5b + 1.
11.Simplify 5 − 2(3c − 4) + c.
12.Simplify −3(2m + 1) + 4(m − 5).

Check Your Understanding

Use what you know about terms and the distributive property to complete these problems.

13.Simplify 8 + 2(3p − 4) − 5p.
14.A student simplifies 4(2x − 3) as 8x − 3. What should the simplified expression be, and what multiplication step did the student miss?
15.Write an expression with at least four terms that simplifies to 6x + 9, then show how you combine its like terms.

3 printable pages

  • Simplifying Algebraic Expressions, page 1 of 3: Recognize Like Terms

    Page 1

  • Simplifying Algebraic Expressions, page 2 of 3: Combine Like Terms, Use the Distributive Property

    Page 2

  • Simplifying Algebraic Expressions, page 3 of 3: Check Your Understanding

    Page 3

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