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Simplifying Algebraic Expressions

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Simplifying Algebraic Expressions

Group terms with the same variable part, then add or subtract their coefficients. When expanding brackets, multiply every term inside by the factor outside.

Like terms

Like terms have identical variable parts. Constants are like terms with no variables.

1.In 6r + 2s + 9r + 4, list the like terms in groups.
2.Which pairs are like terms? Select every correct pair.
  • 4p and 11p
  • 3a and 3a²
  • 8mn and 2mn
  • 6t and 6u
  • 5 and 12

Combine like terms

Collect the matching terms and simplify each expression.

3.Simplify 8x + 5x.
4.Simplify 14b − 6b + 3b.
5.Simplify 7m + 4n + 2m − n.
6.Simplify 5c + 3d − 2c + 6d.
7.Show how to simplify 13x + 4y − 7x + 9y.

Expand brackets

Multiply the outside factor by each term inside the brackets.

8.Expand 4(x + 7).
9.Expand 3(2k − 5).
10.Which expression is equivalent to 5(2a + 3)?
  • 10a + 3
  • 7a + 15
  • 10a + 15
  • 2a + 15
11.Expand and simplify 2(3p + 4) + 5p. Show your working.

Mixed practice and problem solving

Expand brackets where needed, then collect like terms.

12.Simplify 6x + 4y + 3x − y.
13.Simplify 3(q + 5) + 2q.
14.Simplify 4t + 2(3t − 6).
15.Match each expression to its simplified form: 1) 9x + 2x; 2) 3(y + 4); 3) 6a − 2a + 7; 4) 2(2m + 3) + m; 5) 5r + 2(r − 1).
  • 1) 9x + 2x
  • 2) 3(y + 4)
  • 3) 6a − 2a + 7
  • 4) 2(2m + 3) + m
  • 5) 5r + 2(r − 1)
  • B) 11x
  • C) 3y + 12
  • E) 5m + 6
  • A) 7r − 2
  • D) 4a + 7
16.Anahera has x dollars. Arlo has twice Anahera’s amount, plus $7. Write and simplify an expression for their total money.
17.A rectangle has length (2x + 5) cm and width (x + 3) cm. Write and simplify an expression for its perimeter.

Challenge

Check each step carefully, especially when a bracket contains more than one variable term.

18.Expand and simplify 2(4x + 3y) + 3(x − y) + 2x.
19.True or false: 3(5n − 2) is equivalent to 15n − 6. Give one line of working to support your choice.
TrueFalse
20.Which expression simplifies to 8x + 9?
  • 2(3x + 4) + 2x + 1
  • 4(2x + 3) − 4
  • 3(2x + 3) + x
  • 5x + 3x + 8

4 printable pages

  • Simplifying Algebraic Expressions, page 1 of 4: Like terms, Combine like terms

    Page 1

  • Simplifying Algebraic Expressions, page 2 of 4: Expand brackets, Mixed practice and problem solving

    Page 2

  • Simplifying Algebraic Expressions, page 3 of 4: 13. Simplify 3(q + 5) + 2q.

    Page 3

  • Simplifying Algebraic Expressions, page 4 of 4: Challenge

    Page 4

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