1. ©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

2. 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)

3. 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

4. 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

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

6. 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)