Learn: Factorising Single Brackets

Welcome!Today, we will learn how to factorise algebraic expressions using single brackets. This is an essential skill in algebra and will help simplify expressions and solve equations more easily.

What is Factorising?Factorising means rewriting an expression as a product of its factors. It’s the reverse of expanding brackets. It’s useful for simplifying equations and solving problems.

Finding the Highest Common Factor (HCF)The HCF is the largest number or term that divides evenly into all parts of an expression. To factorise, you first identify the HCF of the terms in the expression.

How to Factorise a Single BracketTo factorise a single bracket, follow these steps:Step 1: Identify the HCF of all the terms in the expression.Step 2: Divide each term in the expression by the HCF.Step 3: Write the HCF outside the bracket and the simplified terms inside the bracket.

Example: Factorising 6x + 12Step 1: Identify the HCF of 6 and 12. The HCF is 6.Step 2: Divide each term by 6: 6x ÷ 6 = x and 12 ÷ 6 = 2.Step 3: Write the factorised form: 6(x + 2).

Factorising Expressions with VariablesWhen factorising expressions with variables, consider both the numerical HCF and the highest power of each variable common to all terms. For instance, in 10x² + 5x, the HCF is 5x.

Example: Factorising 10x² + 5xStep 1: The numerical HCF is 5, and the variable HCF is x.Step 2: Divide each term by 5x: 10x² ÷ 5x = 2x, and 5x ÷ 5x = 1.Step 3: Write the factorised form: 5x(2x + 1).

Review Time!Great work! You've learned how to factorise single brackets by finding the HCF and rewriting the expression as a product of factors. Let’s test your understanding with some review questions.