©G Dear 2008 – Not to be sold/Free to use Mathematic (Preliminary) Basic Arithmetic Sum & Difference Of Two Cubes Stage 6 - Year 11 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use

Factorisation a3 + b3 = (a + b) (a2 - ab + b2) Sum & Difference of two Cubes a3 + b3 = (a + b) (a2 - ab + b2) a3 - b3 = (a - b) (a2 + ab + b2)

Factorisation Sum of two Cubes (a + b) (a2 - ab + b2) = a (a2 - ab + b2) + b (a2 - ab + b2) = a3 - a2b +ab2 + a2b – ab2 + b3 = a3 + b3 (a + b) (a2 - ab + b2) = a3 + b3

Difference of two Cubes Factorisation Difference of two Cubes (a - b) (a2 + ab + b2) = a (a2 + ab + b2) - b (a2 + ab + b2) = a3 + a2b +ab2 - a2b - ab2 - b3 = a3 - b3 (a - b) (a2 + ab + b2) = a3 - b3

Factorisation a3 + b3 = (a + b) (a2 - ab + b2) Sum of two Cubes Example m3 + 27 = (m)3 + (3)3   a b = (m + 3)(m2 – 3m + 32) = (m + 3)(m2 – 3m + 9)

Difference of two Cubes Factorisation Difference of two Cubes a3 - b3 = (a - b) (a2 + ab + b2) Example 125e3 - 8 = (5e)3 - (2)3   a b = (5e - 2)[(5e)2 + 5ex2 + 22)] = (5e - 2)(25e2 + 10e + 4)