Simplifying Algebraic Expressions

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📚 Part 1: Key Terms and Understanding

1. Match each algebraic term to its correct definition:

a) Variable _____________ (A number that stands alone)

b) Coefficient _____________ (A letter representing an unknown value)

c) Constant _____________ (Terms that have the same variable part)

d) Like terms _____________ (The number in front of a variable)

2. Circle the like terms in each expression:

a) 3x + 2 + 5x - 1

b) 4y - 3 + 2y + 7

c) 2a + 3b - a + 5b

3. Which of these expressions are already simplified?

5x + 3

2x + 4x

7y - 2

3a + 2 + a

✏️ Part 2: Simplifying Expressions

4. Simplify these expressions by collecting like terms:

a) 2x + 3x = _______

b) 5y - 2y = _______

c) 4a + 2 + 3a = _______

d) 6b - 3 + 2b + 1 = _______

5. Simplify these more challenging expressions:

a) 5x - 2x + 4 - 1 = _____________

b) 3y + 7 - y + 2 = _____________

c) -2a + 5 + 4a - 3 = _____________

d) 8m - 3m - 2 + 6 = _____________

6. Show your working to simplify: 4x + 3 - 2x + 5 - x

🎯 Part 3: Problem Solving

7. Sarah has some apples (represented by x). She starts with 3x apples, buys 2x more, then gives away x apples. Write and simplify an expression for how many apples she has left.

8. A rectangle has length (4y + 2) metres and width (y + 3) metres. If the perimeter formula is 2 × length + 2 × width, write and simplify an expression for the perimeter.

9. When x = 3, calculate the value of your simplified expression from question 6.