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Algebra Expressions Revision Worksheet

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Algebra Expressions Revision Worksheet

Algebra expressions illustration

📚 Part 1: Simplifying and Expanding

1. Simplify these expressions by collecting like terms:

a) 3x + 5x - 2x = ___________

b) 4a + 7b - 2a + 3b = ___________

c) 2m² + 5m - 3m² + 8m = ___________

2. Expand these brackets:

a) 4(x + 3) = ___________

b) -2(3y - 5) = ___________

c) 3(2a + 4b - 1) = ___________

3. Which expression is equivalent to 5(x - 2) + 3x?

8x - 10

8x - 2

5x - 7

8x + 10

4. Factorise these expressions:

a) 6x + 9 = ___________

b) 4y - 12 = ___________

c) 15a + 10b = ___________

🔢 Part 2: Substitution and Evaluation

5. If x = 4 and y = -2, find the value of these expressions:

a) 3x + 5 = ___________

b) 2y - 7 = ___________

c) x² + 3y = ___________

d) 4x - 2y + 1 = ___________

6. The expression 2n + 15 represents the cost in dollars of hiring a trailer for n days. How much would it cost to hire the trailer for:

a) 3 days? $___________

b) 7 days? $___________

c) If the total cost was $35, how many days was the trailer hired? ___________

7. Check all expressions that are equivalent to 12x - 8:

4(3x - 2)

2(6x - 4)

8x + 4x - 8

10x + 2x - 8

🧩 Part 3: Problem Solving

8. A rectangle has length (2x + 5) metres and width (x - 1) metres.

a) Write an expression for the perimeter: ___________

b) Simplify your expression: ___________

c) If x = 8, what is the actual perimeter? ___________

9. Tom thinks of a number, multiplies it by 3, then subtracts 7. His answer is the same as when he adds 5 to twice his original number.

a) If his number is n, write an expression for "multiply by 3, then subtract 7": ___________

b) Write an expression for "add 5 to twice the number": ___________

c) These expressions are equal. Write this as an equation: ___________

10. Explain in your own words what it means to "expand brackets" and give an example:

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