Algebraic Expressions
Understanding Practice Sheet — Think before you simplify!
Important: Show your working wherever required. Do not use a calculator.
The aim is to check whether you understand why the operation works, not just whether you can get an answer.
A. Identify Before You Calculate
1. Circle the like terms in each group:
(a) 3x, −5x, 7y, 2x²
(b) 4a², −3a, 8a², 5ab
(c) 6pq, −2qp, 3p, 9pq
2. Are the following like or unlike terms? Give a reason.
(a) 5x² and −8x²
(b) 7x and 7x²
(c) 3ab and −9ba
3. Without simplifying, predict how many terms will remain after combining:
4x² + 3x − 7x² + 5 − 2x + 9
B. Addition and Subtraction — Do You Really Understand?
4. Simplify:
7x + 3x − 5x5. Simplify:
4a² + 7a − 2a² + 3a6. Simplify:
9p − 4q + 3p + 8q7. A student says:
3x² + 4x² = 7x⁴
Is the student correct? Explain the mistake.
8. Fill in the blank:
5x + ____x = 12x
Then explain how you found it.
C. Opening Brackets — Sign Sense Test
9. Open the brackets:
(a) 3(x + 5)
(b) 4(2x − 3)
(c) −(5x + 7)
(d) −(3x − 8)
10. Simplify completely:
(a) 5x + (3x − 7)
(b) 8y − (3y + 4)
(c) 6a − (2a − 5)
11.
Spot the error:
A student writes:
7x − (2x − 3) = 7x − 2x − 3 = 5x − 3
Identify exactly where the error occurs and give the correct result.
D. Multiplication — Structure Matters
12. Multiply:
(a) 3x × 4x
(b) −2a × 5b
(c) 4x(2x − 3)
13. Expand and simplify:
(x + 3)(x + 5)
14. Which method is appropriate?
3(x + 4) /
(x + 2)(x + 5)
Explain why the two expressions require different multiplication steps.
E. Algebraic Fractions — Think, Then Simplify
17. Complete the rule:
To divide by a fraction, we ________ → ________ → ________.
18. Simplify:
(3x/4y) ÷ (9x²/8y³)
Show the KEEP → CHANGE → FLIP step.
19. Can you cancel the x in the following expression? Explain.
(x + 5)/x
F. Challenge — Diagnose the Thinking
20. Without fully calculating, decide whether each statement is
True or False. Correct the false ones.
(a) 3x + 4y = 7xy
(b) 5x − (2x − 1) = 3x + 1
(c) 2x × 3x² = 6x³
(d) (x + 4)² = x² + 16
21. Find the missing value:
4x + 7 − ____ = 2x + 3
Here the blank represents an algebraic expression. Find it.
22. Create your own expression containing:
• two like terms
• two unlike terms
• one pair of brackets
Then simplify your expression.
G. Exit Check — One-Minute Recall
1. What makes two terms like terms?
2. What happens to signs after a minus before a bracket?
3. What does “distribute” mean?
4. What is the rule for division by a fraction?
🔒 Teacher Answer Key — click only when checking
1. (a) 3x, −5x (b) 4a², 8a² (c) 6pq, −2qp, 9pq
2. (a) Like — same variable and power. (b) Unlike — powers differ. (c) Like — ab and ba represent the same product.
3. Three terms: x², x and constant.
4. 5x
5. 2a² + 10a
6. 12p + 4q
7. False. Correct: 7x². Exponents are not added during addition.
8. 7
9. (a) 3x + 15 (b) 8x − 12 (c) −5x − 7 (d) −3x + 8
10. (a) 8x − 7 (b) 5y − 4 (c) 4a + 5
11. The − sign must change both signs inside. Correct: 5x + 3.
12. (a) 12x² (b) −10ab (c) 8x² − 12x
13. x² + 8x + 15
14. First is a monomial multiplied by a binomial; second is binomial × binomial, requiring four products.
15. 2x
16. 2a²
17. Keep → Change → Flip
18. 2y²/(3x)
19. No. x is not a common factor of x + 5.
20. (a) False: unlike terms cannot combine. (b) True. (c) True. (d) False: x² + 8x + 16.
21. 2x + 4
22. Answers will vary; expression must satisfy all conditions and simplify correctly.