We will do questions of these identities
- Identity VI - (a + b) ^{ 3 } = a ^{ 3 } + b ^{ 3 } + 3ab(a + b)
- Identity VII - (a − b) ^{ 3 } = a ^{ 3 } - b ^{ 3 } - 3ab(a - b)
Check Algebra Formulas for full list of formulas
Lets take an example
Identity VI - (a + b) ^{ 3 } = a ^{ 3 } + b ^{ 3 } + 3ab(a + b)
(2 + 3) ^{ 3 } = 2 ^{ 3 } + 3 ^{ 3 } + 3(2)(3) (2 + 3)
(5) ^{ 3 } = 8 + 27 + 18 × 5
125 = 8 + 27 + 90
125 = 125
Identity VII - (a − b)3 = a3 - b3 - 3ab(a - b)
(2 – 3)3 = 23 – 33 – 3(2)(3) (2 – 3)
(–1)3 = 8 – 27 – 18 × (–1)
–1 = 8 – 27 + 18
–1 = 26 – 27
–1 = –1