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Algebraic Expressions Practice

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Algebraic Expressions Practice

A puzzle room uses algebra to protect its final lock. Simplify, expand and divide expressions to reveal the codes. Show your working for calculation questions.

Clue 1: Collect like terms

Combine terms with the same variable and power. Constants can only be combined with constants.

1.The first lock displays 7x + 4x − 3x. Simplify the expression to find its coefficient of x.
2.A second lock shows 3a² + 5a − 2a + 6 − a². Which expression is its simplified form?
  • 2a² + 3a + 6
  • 2a² + 7a + 6
  • 4a² + 3a + 6
  • 2a² + 3a + 4
3.True or false? In 5p + 2q − 3p, the terms 5p and −3p are like terms, so the expression simplifies to 2p + 2q.
TrueFalse

Clue 2: Expand the brackets

Multiply every term inside the bracket. Then collect any like terms.

4.The keypad's expression is 3(2x − 5) + x. Expand and simplify it.
5.Expand and simplify the expression (x + 6)(x − 2), found on a folded clue.
6.A code card shows (2m + 3)(m − 4). Which is the expanded and simplified expression?
  • 2m² − 5m − 12
  • 2m² − 8m + 3
  • 2m² + 11m − 12
  • 2m² − 5m + 12

Clue 3: Divide and decode

Use the laws of indices for monomials. For polynomial division, factor the numerator first when possible.

7.The box's first division code is 12x⁴ ÷ 3x². Simplify it.
8.Simplify (x² − 25) ÷ (x − 5), for x ≠ 5. Show how factoring the numerator helps.
9.For the final check, simplify (18ab²) ÷ (6ab), assuming a and b are non-zero.
10.A teammate says (x + 3)² = x² + 9. Is this correct? Explain the expansion and give the correct expression.

2 printable pages

  • Algebraic Expressions Practice, page 1 of 2: Clue 1: Collect like terms, Clue 2: Expand the brackets

    Page 1

  • Algebraic Expressions Practice, page 2 of 2: Clue 3: Divide and decode

    Page 2

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