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2.2 Simplifying Expressions

GCSE Maths Foundation · Edexcel · Chapter 2: Expressions

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: multiplying and dividing terms, and using powers in algebra. 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

  • Multiply terms such as 3a × 4b and write the answer in its simplest form
  • Write repeated letters using powers, e.g. y × y × y = y³
  • Divide terms such as 15ab ÷ 5a
  • Simplify expressions for areas and volumes

Key words

  • Simplify: Write an expression in a shorter, neater way without changing its value.
  • Product: The result of multiplying. The product of 3a and 4b is 12ab.
  • Power (index): Shows repeated multiplication: p × p × p = p³.
  • Coefficient: The number part of a term. In 12ab the coefficient is 12.

Multiplying terms

Multiply the numbers first, then write the letters next to each other in alphabetical order. Leave out the × signs.

Worked example: multiplying

(a) 4 × 3m = 12m (b) 2a × 5b = 10ab
(c) 3p × 2q × r = 6pqr (d) −2x × 7y = −14xy

Answer: 12m, 10ab, 6pqr, −14xy

Powers in algebra

When the same letter is multiplied, use a power. a × a = a² and y × y × y = y³. To multiply powers of the same letter, add the indices.

Worked example: letters with powers

(a) 2x × 3x = 6x²
(b) p² × p³ = p⁵ (because p × p × p × p × p)
(c) 4y² × 3y = 12y³

Answer: 6x², p⁵, 12y³

Key fact: x + x = 2x but x × x = x². Adding and multiplying give different answers.

Dividing terms

Write the division as a fraction. Divide the numbers, then cancel letters that appear on the top and the bottom.

Worked example: dividing

(a) 12x ÷ 3 = 4x
(b) 15ab ÷ 5a = (15 ÷ 5) × (ab ÷ a) = 3b
(c) 18x² ÷ 6x = 3x (x² ÷ x = x)

Answer: 4x, 3b, 3x

Mixed problems

Do the multiplying and dividing first, then collect like terms.

Worked example: multiply then collect

Simplify 3a × 2b + 4ab
3a × 2b = 6ab, then 6ab + 4ab = 10ab

Answer: 10ab

Worked example: area of a square

A square has sides of length 5t cm. Find its area.
Area = 5t × 5t = 25t²

Answer: 25t² cm²

Common mistakes

  • Adding when you should multiply: 3x × 4x is 12x², not 7x or 12x.
  • Multiplying powers instead of adding: p³ × p² = p⁵, not p⁶.
  • Forgetting to divide the letters: 15ab ÷ 5a is 3b, not 3ab.
  • Writing the letters before the number: write 12ab, not ab12.

Revision questions

Try these, then check your answers below each one.

Question 1. Simplify 3a × 4b. (Choose from: 12ab, 7ab, 12a + b, 34ab.)

Answer: 12ab

Working: 3 × 4 = 12 and a × b = ab, so 12ab.

Question 2. Simplify 5x × 2x. (Choose from: 10x², 10x, 7x², 25x.)

Answer: 10x²

Working: 5 × 2 = 10 and x × x = x², so 10x².

Question 3. Simplify 18y ÷ 3.

Answer: 6y

Working: 18 ÷ 3 = 6, so 18y ÷ 3 = 6y.

Related lessons

Continue in the full course

This lesson is section 2.2 (EGCMF0202) 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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