Topic Review — Algebraic Expressions

Review Questions

1. Like terms and simplifying. Fluency

   1. Simplify: 9x + 4x − 3x
   2. Simplify: 6a + 3b − 2a + 5b
   3. Simplify: 5m² − 3m + 2m² + m
   4. Identify the like terms in: 4x, 3y, 7x, 2x², 5y, x²
   5. Simplify: 3pq + 5p − pq + 2p
   6. Simplify: 7t² − 4t + 3 − 2t² + 6t − 1

2. Expanding with the distributive law. Fluency

   1. Expand: 3(5x + 4)
   2. Expand: −2(3y − 8)
   3. Expand: 4a(2a + 7)
   4. Expand and simplify: 5(x + 3) + 2(x − 1)
   5. Expand and simplify: 3(2m − 4) − (m + 2)
   6. Expand and simplify: 2n(n + 4) − 3n(n − 2)

3. Factorising algebraic expressions. Fluency

   1. Factorise: 6x + 10
   2. Factorise: 9y − 12
   3. Factorise: 8a² + 20a
   4. Factorise: 15m² − 10m
   5. Factorise: 6p² + 9p − 3
   6. Factorise: −4t² − 8t

4. Substitution and mixed operations. Understanding

   1. If x = 5, evaluate: 3x² − 4x + 2
   2. If a = −3, evaluate: 2a + a²
   3. Expand 4(3k − 2) + 5k, then evaluate when k = 2.
   4. Factorise 12x + 18, then verify by expanding.
   5. A student claims that 3(x + 4) = 3x + 4. Show this is incorrect by expanding correctly, and find a value of x where both expressions give different results.
   6. Expand and simplify: 2(x + 3)² is not required, but simplify 2x(x + 3) − x(2x − 1).

5. Mixed algebraic problem solving. Problem Solving

   1. A rectangle has length (4x + 3) cm and width 5 cm.
      1. Write and simplify an expression for the perimeter.
      2. Find the perimeter when x = 2.
   2. A rectangular garden has area (12x² + 8x) m². Factorise this expression to find two possible dimension expressions for the garden.
   3. The cost of hiring a bike is $5 plus $3 per hour. Write an expression for the total cost after h hours. Expand and evaluate for h = 4 hours.
   4. Two friends simplify 2(3a + 1) − 4a:
      • Friend 1 gets: 2a + 2
      • Friend 2 gets: 2a − 2
      Who is correct? Show full working.