Expressions and Formulae

Expressions and Formulae

1. Simplifying expressions

   • Simplifying expressions with one variable: Xa + Ya + Za = (X + Y + Z)a e.g. 15a – (5a + 6a) = 15a – 11a = 4a
   • Simplifying expressions with multiple variables: Wb + Xa + Ya + Zb = (X + Y)a + (W + Z)b e.g. 15a + 6b – (5b + 6a) = (15a – 6a) + (6b - 5b) = 9a + b

2. Expanding brackets

   • x(a + b) = xa + xb . 2x(4 + 2) = 2x(6) = 12x .

3. Factorising brackets

   • Use highest common factors of all the numbers in an expression / a formula to see what you should factorise with. For example if it is 6x + 4xy you can factorise to make it 2x(3 + 2y) because 2x is the HCF. 16x_ + 4x = 4x(4x + 1)
   • Difference of two squares: If a formula is Ax_ - y_ then you can factorise as (x+y)(Ax - y) or ( Ax +y)( Ax - y)

4. Quadratic equations

   • 2x_ + 8x +8 = (2x + 4)(x+2) because 4*2=8 and 4 + (2*2) = 8