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GRADE 7 · MATHEMATICS · ALGEBRA

Simplifying Algebraic Expressions

Learn how to make algebraic expressions shorter and easier to work with. Identify variables, coefficients and like terms, collect terms carefully, and use the distributive property without changing the value of an expression.

Learning time: approximately 25–30 minutes · Building algebra foundations

What You Will Learn

1. What Is an Algebraic Expression?

An algebraic expression is a mathematical phrase made from numbers, variables and operation signs. Unlike an equation, an expression does not contain an equals sign that states two sides are equal.

Example: In 4x + 7, the letter x is a variable, 4 is its coefficient, and 7 is a constant. The expression has two terms: 4x and 7.
Variable

A letter representing a number, such as x or n.

Coefficient

The number multiplying a variable. In 6y, the coefficient is 6.

Constant

A number without a variable, such as 9 in 3x + 9.

Term

A part separated by plus or minus signs. In 2a − 5, the terms are 2a and −5.

2. Like Terms and Unlike Terms

Like terms have exactly the same variable part, including the same variables raised to the same powers. Their coefficients may be different.

TermsCan they be combined?Reason
3x and 8xYesBoth have x.
4a and −2aYesBoth have a.
5y and 5zNoDifferent variables.
2x and 2x²NoDifferent powers of x.
7 and −3YesBoth are constants.
Remember: You can combine 3x and 5x, but you cannot combine 3x and 5y into 8xy or 8x. Unlike terms stay separate.

3. Combine Like Terms

Add or subtract the coefficients and keep the common variable part unchanged.

Worked example 1: 3x + 5x

IdentifyBoth terms contain x.
Combine coefficients3 + 5 = 8
Keep the variable3x + 5x = 8x

Worked example 2: 9a − 4a + 2

  1. Combine the a terms: 9a − 4a = 5a.
  2. The constant 2 has no like variable term, so it stays.

Simplified expression: 5a + 2.

Worked example 3: 6m + 3 − 2m + 8

  1. Group variable terms: 6m − 2m = 4m.
  2. Group constants: 3 + 8 = 11.

Simplified expression: 4m + 11.

4. Work Carefully with Negative Coefficients

A minus sign belongs to the term that follows it. Keep it when collecting coefficients.

Worked example: 5x − 8x + 6

  1. Combine the variable terms: 5x − 8x = (5 − 8)x.
  2. Calculate the coefficient: 5 − 8 = −3.
  3. Keep the constant 6.

Simplified expression: −3x + 6.

Another example: 4p − 7 + 2p − 5 = (4p + 2p) + (−7 − 5) = 6p − 12.

5. The Distributive Property

The distributive property means multiplying the number outside brackets by every term inside the brackets.

Rule: a(b + c) = ab + ac

Worked example 1: 3(x + 4)

Multiply each term3 × x and 3 × 4
Write the result3x + 12

Worked example 2: 5(2y − 3)

  1. Multiply 5 by 2y: 10y.
  2. Multiply 5 by −3: −15.

Expanded expression: 10y − 15.

Worked example 3: −2(a + 6)

Multiply −2 by both terms: (−2 × a) + (−2 × 6) = −2a − 12.

Common error: In 4(x + 3), do not multiply 4 by x but forget the 3. The correct expansion is 4x + 12.

6. Expand and Then Simplify

Sometimes an expression contains brackets and like terms. Expand first, then collect like terms.

Worked example: 2(x + 3) + 4x − 5

Expand brackets2x + 6 + 4x − 5
Collect variable terms2x + 4x = 6x
Collect constants6 − 5 = 1
Final result6x + 1

7. Evaluate an Expression

To evaluate an expression, replace each variable with its given value, then follow the order of operations.

Worked example: Evaluate 3x + 2 when x = 4

  1. Substitute 4 for x: 3(4) + 2.
  2. Multiply first: 12 + 2.
  3. Add: 14.

Value: 14.

Worked example: Evaluate 2a − 3b when a = 5 and b = 2

Substitute: 2(5) − 3(2) = 10 − 6 = 4.

8. Common Mistakes to Avoid

Combining unlike terms: 2x + 3y cannot be simplified to 5xy. The terms have different variables.
Dropping a negative sign: In 4x − 7x, the coefficient calculation is 4 − 7 = −3, so the result is −3x.
Distributing to only one term: Multiply the outside factor by every term inside the brackets.
Confusing a coefficient with a power: 5x means 5 multiplied by x. It does not mean x to the power 5.
Ignoring order of operations: When evaluating, calculate multiplication before addition or subtraction.

9. Practice Exercises

Simplify each expression. For the evaluation questions, substitute the given values.

  1. 4x + 7x
  2. 9a − 3a + 5
  3. 6m + 4 − 2m + 7
  4. 8p − 11p
  5. 3(y + 5)
  6. −4(2x − 3)
  7. 2(a + 4) + 3a − 1
  8. Evaluate 5n − 2 when n = 3.
Show practice answers and working
  1. 11x. Add the coefficients 4 + 7.
  2. 6a + 5. Combine 9a − 3a.
  3. 4m + 11. Combine 6m − 2m and 4 + 7.
  4. −3p. Calculate 8 − 11.
  5. 3y + 15. Multiply 3 by both terms in brackets.
  6. −8x + 12. Multiply −4 by 2x and by −3.
  7. 5a + 7. Expand to 2a + 8 + 3a − 1, then combine.
  8. 13. Substitute 3: 5(3) − 2 = 15 − 2.

10. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

1. Simplify: 3x + 6x.
2. Which pair contains like terms?
3. Expand: 4(x + 2).
4. Simplify: 5x − 8x + 3.
5. Evaluate 2a + 1 when a = 4.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 7 Mathematics

Simplifying Algebraic Expressions Worksheet

Name: __________________________ Date: _______________

Instructions: Show your steps and combine only like terms.

  1. 7x + 2x − 4x
  2. 5a + 8 − 2a + 3
  3. 6( y − 2 )
  4. −3(2m + 5)
  5. 4(p + 2) + 3p − 1
  6. Evaluate 3x + 4 when x = 6.
  7. Explain why 3x and 3y are unlike terms.

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. 5x.
  2. 3a + 11.
  3. 6y − 12.
  4. −6m − 15.
  5. 7p + 7.
  6. 22.
  7. They have different variables, so they cannot be combined.

12. Lesson Summary

Next step: Use simplified expressions when solving equations. The next algebra lessons build on these skills.

Educational note: This is a curriculum-neutral Grade 7 lesson. Teachers and parents can adapt examples and practice to their local curriculum.

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