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Science
Simplifying Algebraic Expressions
Year 7 • Algebra
Lesson: Simplifying Expressions
Learn how to simplify algebraic expressions step-by-step by collecting like terms, working with brackets, and avoiding common mistakes – perfect for Year 7 UK students.
Lesson Objectives
- Understand what an algebraic expression is.
- Identify like and unlike terms.
- Simplify expressions by collecting like terms.
- Simplify simple expressions with brackets using the distributive law.
1. What Is an Algebraic Expression?
An algebraic expression is a combination of numbers, letters (variables), and operations such as +, −, × and ÷.
Examples of algebraic expressions:
3x + 5
2y − 7
4a + 3b − 2
5n − 3n + 8
3x + 5
2y − 7
4a + 3b − 2
5n − 3n + 8
2. Like Terms and Unlike Terms
Like terms are terms that have the same variable part (same letter, same power). Unlike terms have different variable parts.
Like terms
3x and 5x
2y and −7y
4a and −9a
6 and −2 (both constants)
3x and 5x
2y and −7y
4a and −9a
6 and −2 (both constants)
Unlike terms
3x and 3y
2a and 2a²
5b and 5c
x and 4
3x and 3y
2a and 2a²
5b and 5c
x and 4
3. Simplifying by Collecting Like Terms
To simplify an expression, we combine (add or subtract) the coefficients of like terms.
Example 1:
Simplify: 3x + 5x
→ (3 + 5)x = 8x
Example 2:
Simplify: 7y − 2y
→ (7 − 2)y = 5y
Example 3:
Simplify: 4a + 3 − 2a + 5
Group like terms: (4a − 2a) + (3 + 5)
→ 2a + 8
Simplify: 3x + 5x
→ (3 + 5)x = 8x
Example 2:
Simplify: 7y − 2y
→ (7 − 2)y = 5y
Example 3:
Simplify: 4a + 3 − 2a + 5
Group like terms: (4a − 2a) + (3 + 5)
→ 2a + 8
4. Simplifying Expressions with Brackets
We use the distributive law to remove brackets:
a(b + c) = ab + ac
Examples:
2(x + 3) = 2x + 6
3(2y − 1) = 6y − 3
5(a + 4) = 5a + 20
2(x + 3) = 2x + 6
3(2y − 1) = 6y − 3
5(a + 4) = 5a + 20
5. Real-Life Style Example
A shop sells pens and pencils. One pen costs £x and one pencil costs £2.
(a) Write an expression for buying 3 pens and 4 pencils.
→ 3x + 4 × 2 = 3x + 8
(b) Another customer buys 2 pens and 1 pencil: 2x + 2. Simplify the total cost for both customers together:
(3x + 8) + (2x + 2) = (3x + 2x) + (8 + 2) = 5x + 10
Practice Questions
A. Like and Unlike Terms
In each list, circle or underline the like terms:
- 3x, 5x, 2y, 7
- 4a, 6, 9a, 6a
- 5b, 3c, 2b, b
B. Simplify the Expressions
Simplify each expression by collecting like terms:
- 4x + 3x
- 7y − 2y
- 5a + 2a − a
- 3n + 4 + 2n
- 6p − 3p + 5
C. Simplify with Negative Terms
- 8x − 3x
- 10y − 4y − 2y
- 5a − a + 3a
- 9b − 2 − 3b
D. Simplify Expressions with Brackets
Expand the brackets and simplify:
- 2(x + 4)
- 3(y + 5)
- 4(a − 2)
- 5(n + 1) + n
E. Word Problems
-
A cinema ticket costs £t.
A family buys 3 tickets for adults and 2 tickets for children at the same price t.
Write and simplify an expression for the total cost. - A school sells maths workbooks. One workbook costs £x and one ruler costs £3. A student buys 2 workbooks and 3 rulers. Write and simplify an expression for the total cost.
✅ Show Answer Key
A. Like and Unlike Terms
- Like terms: 3x and 5x (2y and 7 are different types)
- Like terms: 4a, 9a, 6a (6 is a constant)
- Like terms: 5b, 2b, b (3c is different)
B. Simplify the Expressions
- 4x + 3x = 7x
- 7y − 2y = 5y
- 5a + 2a − a = (5 + 2 − 1)a = 6a
- 3n + 4 + 2n = (3n + 2n) + 4 = 5n + 4
- 6p − 3p + 5 = (6p − 3p) + 5 = 3p + 5
C. Simplify with Negative Terms
- 8x − 3x = 5x
- 10y − 4y − 2y = (10 − 4 − 2)y = 4y
- 5a − a + 3a = (5 − 1 + 3)a = 7a
- 9b − 2 − 3b = (9b − 3b) − 2 = 6b − 2
D. Brackets
- 2(x + 4) = 2x + 8
- 3(y + 5) = 3y + 15
- 4(a − 2) = 4a − 8
- 5(n + 1) + n = (5n + 5) + n = 6n + 5
E. Word Problems
- 3 tickets + 2 tickets = 5 tickets at price t each → total cost = 5t.
- 2 workbooks: 2x 3 rulers: 3 × 3 = 9 Total cost = 2x + 9 (already simplified).
© Aviate Learning – Simplifying Expressions (Year 7)