Algebra factorising is a fundamental concept in GCSE Mathematics that involves breaking down algebraic expressions into simpler forms. The process involves finding the common factors of the terms in an expression and then grouping them together, thereby reducing the overall complexity of the expression. Factorising is an essential skill in algebra, as it allows us to simplify equations, solve equations, and identify patterns and relationships between different expressions.

To factorise an expression, we need to look for the highest common factor (HCF) of the terms in the expression. The HCF is the largest factor that divides evenly into all the terms. Once we have identified the HCF, we can factor it out of each term in the expression, leaving us with a simpler form. For example, consider the expression:

2x² + 4x

To factorise this expression, we need to identify the HCF of the two terms. In this case, the HCF is 2x since both terms have a factor of 2x. We can then factor out 2x from each term:

2x(x + 2)

The factorised form of the expression is 2x(x + 2). This form is more straightforward than the original expression and can be used in various algebraic operations such as simplification, substitution, or solving equations.

Let's consider another example:

3xy - 6x

To factorise this expression, we must first identify the HCF of the two terms. In this case, both terms have a factor of 3x, so we can factor out 3x: