Year 8 Simplifying Expressions (Like Terms) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

Download answers PDF Print answers Back to worksheet

Year 8 · Mathematics · Algebraic Expressions

Year 8 Simplifying Expressions (Like Terms) Worksheet — Level 3 — Answers

Success Tutoring

Collect the like terms. Only terms with exactly the same letter and power can be added.

1.Simplify: 4x + 3y² + 8x + 3y²

Answer: 12x + 6y²

x terms: 4x + 8x = 12x
y² terms: 3y² + 3y² = 6y²

2.Simplify: −2x − 6y + 2x + 8y

Answer: 2y

x terms: −2x + 2x = 0
y terms: −6y + 8y = 2y

3.Simplify: x + 2y² + 6x + 5y²

Answer: 7x + 7y²

x terms: x + 6x = 7x
y² terms: 2y² + 5y² = 7y²

4.Simplify: 4x − 4y + 5x + 4y

Answer: 9x

x terms: 4x + 5x = 9x
y terms: −4y + 4y = 0

5.Simplify: −3x + 9y² + 6x − 3y²

Answer: 3x + 6y²

x terms: −3x + 6x = 3x
y² terms: 9y² − 3y² = 6y²

6.Simplify: 5x + y + 9x − 5y

Answer: 14x − 4y

x terms: 5x + 9x = 14x
y terms: y − 5y = −4y

7.Simplify: −6x − y² − 5x + 4y²

Answer: −11x + 3y²

x terms: −6x − 5x = −11x
y² terms: −y² + 4y² = 3y²

8.Simplify: 5x + 4y + 5x − 3y

Answer: 10x + y

x terms: 5x + 5x = 10x
y terms: 4y − 3y = y

9.Simplify: −x − 4y − 5x − 5y

Answer: −6x − 9y

x terms: −x − 5x = −6x
y terms: −4y − 5y = −9y

10.Simplify: 7x − 5y + 7x − 3y

Answer: 14x − 8y

x terms: 7x + 7x = 14x
y terms: −5y − 3y = −8y

11.Simplify: 2x + 6y² − 3x + 9y²

Answer: −x + 15y²

x terms: 2x − 3x = −x
y² terms: 6y² + 9y² = 15y²

12.Simplify: 4x − 2y² − 3x − 5y²

Answer: x − 7y²

x terms: 4x − 3x = x
y² terms: −2y² − 5y² = −7y²

13.Simplify: 2x + 9y² + 6x + 9y²

Answer: 8x + 18y²

x terms: 2x + 6x = 8x
y² terms: 9y² + 9y² = 18y²

14.Simplify: −4x − 2y² + 9x + 9y²

Answer: 5x + 7y²

x terms: −4x + 9x = 5x
y² terms: −2y² + 9y² = 7y²

Marking tips

Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: