Algebra factorising is a fundamental skill you will use extensively in GCSE Maths and beyond. It is used to simplify algebraic expressions by breaking them down into smaller parts called factors. Factoring involves identifying a common factor present in all of the terms of an expression and then using this factor to write the expression as a product of simpler expressions.

Factorising is the opposite of expanding brackets, which involves multiplying out brackets to simplify expressions. It is essential to understand both processes to be successful in algebra. The factorisation process allows us to simplify and solve equations more efficiently by reducing the number of terms in the equation.

Factorising involves identifying a factor common to all the terms of the expression and writing it outside the brackets. The remaining terms are then written inside the brackets. For example, consider the expression 3x + 9. Both terms have a common factor of 3, so we can factorise this expression as follows:
3x + 9 = 3(x + 3)

Notice that when we multiply out the brackets, we get back to the original expression:
3(x + 3) = 3x + 9

This process can be applied to more complex expressions, such as 4x2 + 12x. In this case, we can factorise by taking out a common factor of 4x:
4x2 + 12x = 4x(x + 3)

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