Maths Unit 15 – Expand, factorise and change the subject of a formula Expanding a single bracket Expanding double brackets Examples Multiply what is inside the bracket by what is outside the bracket. Be careful with negatives. Expand and simplify (a + 2)(a – 5) Expand and simplify (6b - 2)(b – 1) x x a +2 6b -2 Examples a² 6b² a -5 +2a b -1 +2b Expand 3(p + 2) Expand 5r(6 - r) x x -5a -10 -b +2 p +2 6 -r 3p 5r 30r -5r² 3 +6 a²+ 2a – 5a - 10 a²+ 2a – 5a - 10 3p + 6 30r – 5r² Remember to simplify by putting like terms together Answer = a²- 3a - 10 Remember to simplify by putting like terms together Answer = 6b²+b + 2 Factorising a linear expression This is the opposite of expanding. Here the expression is divided by the highest common factor or factors, the factor or factors are place on the outside of the bracket and the remaining expression is put inside the brackets. Factorising a quadratic expression A quadratic expression is any mathematical expression whose largest power is two. E.g. x² + 5x – 4 Factorising a quadratic means you need to put brackets in. Key words and definitions Expanding – is when the brackets are removed from an expression by multiplying all the terms in the brackets with what is outside the bracket Factorising - is the process of finding the factors that are multiplied to reach a certain number Subject of a formula - It is a variable which is expressed in terms of other variables involved in the formula. Formulae are written so that a single variable, the subject of the formula is on the left hand side of the equation.