Simplify expressions: distribute and combine like terms

Grade 8 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

  1. Kira's hardest card has a bracket inside a bracket: 3[2(x + 4) − x]. How would Kira write it with as few terms as possible?

  2. Luz's hardest card has a bracket inside a bracket: −2[4(x − 2) + x]. How would Luz write it with as few terms as possible?

  3. Milo's hardest card has a bracket inside a bracket: 4[2(x + 3) + 2x]. How would Milo write it with as few terms as possible?

  4. Pia's quilt is a rectangle 3x − 1 units long and x + 4 units wide. What is its perimeter, as an expression with as few terms as possible?

  5. Ren's window is a rectangle 1.5x + 2 units long and 2x − 0.5 units wide. What is its perimeter, as an expression with as few terms as possible?

  6. Tala's door is a rectangle 4x + 1 units long and 2x − 3 units wide. What is its perimeter, as an expression with as few terms as possible?

  7. Zee wants 3(x − ?) − x to equal 2x − 12 for every x. What number goes in the box marked ?

  8. Ari wants 4(x − ?) + 2x to equal 6x − 20 for every x. What number goes in the box marked ?

  9. Bo wants 5(x − ?) − x to equal 4x − 15 for every x. What number goes in the box marked ?

  10. Esme wants 2(x − ?) + 3x to equal 5x − 14 for every x. What number goes in the box marked ?

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Simplify expressions: distribute and combine like terms

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

  1. Kira's hardest card has a bracket inside a bracket: 3[2(x + 4) − x]. How would Kira write it with as few terms as possible?

    3x + 24
  2. Luz's hardest card has a bracket inside a bracket: −2[4(x − 2) + x]. How would Luz write it with as few terms as possible?

    -10x + 16
  3. Milo's hardest card has a bracket inside a bracket: 4[2(x + 3) + 2x]. How would Milo write it with as few terms as possible?

    16x + 24
  4. Pia's quilt is a rectangle 3x − 1 units long and x + 4 units wide. What is its perimeter, as an expression with as few terms as possible?

    8x + 6
  5. Ren's window is a rectangle 1.5x + 2 units long and 2x − 0.5 units wide. What is its perimeter, as an expression with as few terms as possible?

    7x + 3
  6. Tala's door is a rectangle 4x + 1 units long and 2x − 3 units wide. What is its perimeter, as an expression with as few terms as possible?

    12x - 4
  7. Zee wants 3(x − ?) − x to equal 2x − 12 for every x. What number goes in the box marked ?

    4
  8. Ari wants 4(x − ?) + 2x to equal 6x − 20 for every x. What number goes in the box marked ?

    5
  9. Bo wants 5(x − ?) − x to equal 4x − 15 for every x. What number goes in the box marked ?

    3
  10. Esme wants 2(x − ?) + 3x to equal 5x − 14 for every x. What number goes in the box marked ?

    7