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2.1 Algebraic Expressions

GCSE Maths Foundation · Edexcel · Chapter 2: Expressions

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: the language of algebra, writing expressions from words, and collecting like terms. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Use the words term, expression, equation, formula and identity correctly
  • Write an expression from a description in words or a diagram
  • Simplify expressions by collecting like terms
  • Write and simplify expressions for perimeters and in real-life contexts

Key words

  • Variable: A letter that stands for a number that can change, e.g. x or n.
  • Term: A single number, letter, or numbers and letters multiplied, e.g. 5, x, 4ab, 3y².
  • Expression: A group of terms joined by + or −, with no equals sign, e.g. 3x + 2y − 7.
  • Like terms: Terms with exactly the same letters and powers, e.g. 4x and −x, or 2y² and 5y².
  • Coefficient: The number in front of a letter. In 7p the coefficient of p is 7.

The language of algebra

  • Expression; What it is terms with no equals sign; Example 4x − 3
  • Equation; What it is has an equals sign; true only for certain values; Example 4x − 3 = 9 (x = 3)
  • Formula; What it is a rule linking two or more variables; Example P = 4s
  • Identity; What it is true for every value; uses ≡; Example 2(x + 1) ≡ 2x + 2

Worked example: naming

Is each one an expression, an equation or a formula?
(a) 5y + 1 = 16: equation (b) 5y + 1: expression (c) C = 5n + 1: formula

Answer: equation, expression, formula

We leave out the × sign: 3 × a is written 3a, and a × b is ab. Division is written as a fraction: m ÷ 4 is m/4.

Writing expressions

Turn the words into algebra one step at a time.

  • 5 more than n; Expression n + 5
  • 7 less than n; Expression n − 7
  • n multiplied by 3, then subtract 4; Expression 3n − 4
  • add 4 to n, then multiply by 3; Expression 3(n + 4)
  • n divided by 2; Expression n/2

Worked example: shopping

Pens cost p pence each and rulers cost r pence each. Write an expression for the cost of 3 pens and 2 rulers.
3 pens cost 3p and 2 rulers cost 2r.

Answer: 3p + 2r pence

Collecting like terms

Add or subtract like terms only. Each term keeps the sign in front of it. Unlike terms stay separate: 3a + 2b cannot be simplified.

Worked example: two letters

Simplify 5a + 3b − 2a + b
a terms: 5a − 2a = 3a. b terms: 3b + b = 4b

Answer: 3a + 4b

Worked example: squares and numbers

Simplify 4x² + 3x − x² + 5 − 7x
x² terms: 4x² − x² = 3x²
x terms: 3x − 7x = −4x. Number: +5

Answer: 3x² − 4x + 5

Key fact: x and x² are not like terms. Treat them as different letters.

Perimeters and contexts

The perimeter is the total distance round the outside. Add every side, then collect like terms.

Worked example: perimeter

Perimeter = (x + 3) + 2x + (x + 3) + 2x
x terms: x + 2x + x + 2x = 6x. Numbers: 3 + 3 = 6

Answer: 6x + 6 cm

Worked example: ages

Ali is a years old. His sister is 3 years older. His father is twice Ali’s age. Write an expression for their total age.
a + (a + 3) + 2a

Answer: 4a + 3

Common mistakes

  • Joining unlike terms: 4a + 3b is not 7ab.
  • Losing the sign: in 6x − 2y − 8x the 8x is subtracted, so the x terms make −2x.
  • Writing “4 less than m” as 4 − m. It means m − 4.
  • Adding x and x² together. They are not like terms.

Revision questions

Try these, then check your answers below each one.

Question 1. Which expression means “5 less than 3 times n”? (Choose from: 3n - 5, 5 - 3n, 3(n - 5), 3n + 5.)

Answer: 3n - 5

Working: 3 times n is 3n. 5 less than that is 3n - 5.

Question 2. Simplify 7x + 2y - 3x + 5y. (Choose from: 4x + 7y, 10x + 7y, 4x + 3y, 11xy.)

Answer: 4x + 7y

Working: 7x - 3x = 4x and 2y + 5y = 7y, so the answer is 4x + 7y.

Question 3. Is 2x + 5 = 17 an equation?

Answer: Yes

Working: It has an equals sign and is true only when x = 6, so it is an equation.

Related lessons

Continue in the full course

This lesson is section 2.1 (EGCMF0201) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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