Lesson title: Factorising expressions

DO NOW: Copy then answer. Show working

Find the HCF

  1. \(8x\) and \(12\)

  2. \(6a\) and \(15a^2\)

  3. \(10m\) and \(25m^3\)

Expand

  1. \(4(x + 3)\)

  2. \(5a(2 + 3a)\)

  3. \(3m(4 + 5m^2)\)

Today’s learning

By the end of this lesson, you will be able to:

  • Factorise algebraic expressions using HCF
  • Check factorisation by expanding
  • Understand different levels of factorisation

What is factorising?

Copy this definition:

Factorising: Writing an expression as a product of its factors

Example: \(8x + 12 = 4(2x + 3)\)

The expression \(8x + 12\) has been written as factors: \(4\) and \((2x + 3)\)

The factorising method

Copy these steps and the example:

Step 1: Find the HCF of all terms

Step 2: Write HCF outside brackets

Step 3: Divide each term by the HCF to find what goes inside brackets

Always check by expanding your answer

Example: Factorise \(6a + 9\)

Step 1: HCF of 6a and 9 = 3

Step 2: 3(__ + __)

Step 3: 6a ÷ 3 = 2a, 9 ÷ 3 = 3

Answer: 6a + 9 = 3(2a + 3)

Check: \(3(2a + 3) = 6a + 9\) ✓

Your turn

Complete with full working

Q1: \(10x + 15\)

Q2: \(8a^2 + 12a\)

Q3: \(4y + 6\)

Full vs partial factorisation

Copy:

Consider: \(12p + 18\)

Both are factorised:

\(12p + 18 = 6(2p + 3)\)

\(12p + 18 = 2(6p + 9)\)

The first is factorised as much as possible because \(6\) is the HCF.

Practice

Factorise completely. Show all working and check each answer:

  1. \(4y + 8\)

  2. \(9n^2 + 12n\)

  3. \(6x + 15\)

  1. \(14a + 21\)

  2. \(10m^3 + 25m\)

  3. \(18b + 24\)

Common errors

Find the mistake in each solution:

Error 1: \(15x + 20\)

HCF = 5
Answer: 5(15x + 20)

Error 2: \(8a^2 + 12a\)

HCF = 4a
Answer: 4a(2a + 12)

Early finishers: start Ex 3.11 (a,c,e,…)

Summary

Today we learned:

  1. Find HCF of all terms
  2. Write HCF outside brackets
  3. Divide each term by HCF to find what goes inside
  4. Always check by expanding

Next lesson: Factorising with subtraction