Help your students prepare for their Maths GCSE with this free factorising worksheet of 26 questions and answers
Factorising is the inverse of expanding brackets. It involves rewriting an expression so that it becomes the product of two (or more) terms in brackets.
The topic begins with factorising binomials (polynomials with 2 terms) into a single bracket using common factors. This involves skills such as comparing the coefficients of the two terms and considering their highest common factor (hcf). The highest common factor may be a number, a variable (a letter) or both. Both terms may have indices, so an understanding of indices can be very useful.
The topic moves onto factorising trinomials (polynomials with 3 terms) such as quadratic expressions. This leads to rewriting the trinomial as a product of two factors, each with its own set of brackets. This is often referred to as factorising quadratics with double brackets. This can be done by looking at the constant term and finding its factor pairs and calculating which pair sum to make the coefficient of the x term. We can use factorising quadratics as a method for solving quadratic equations.
When a binomial expression involves a square term being subtracted from another square term, we can factorise it by using the difference of two squares method. This results in double brackets. Knowledge of square numbers is useful when factorising using this method.
Looking forward, students can progress with more factorising worksheets to additional algebra worksheets, for example a solving equations worksheet, simultaneous equations worksheet, or a rearranging equations worksheet.
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