Let us discuss some algebra identities and do its formula.
- Identity I - (a + b) ^{ 2 } = a ^{ 2 } + b ^{ 2 } + 2ab
- Identity II - (a − b) ^{ 2 } = a ^{ 2 } + b ^{ 2 } − 2ab
- Identity III - a ^{ 2 } − b ^{ 2 } = (a − b) (a + b)
- Identity IV - (x + a) (x + b) = x ^{ 2 } + (a + b) x + ab
See Algebra Formulas for full list of identities.
Let’s take examples of the identities
Identity I - (a + b) ^{ 2 } = a ^{ 2 } + b ^{ 2 } + 2ab
(2 + 3) ^{ 2 } = 2 ^{ 2 } + 3 ^{ 2 } + 2(2)(3)
5 ^{ 2 } = 4 + 9 + 12
25 = 25
Identity II - (a − b) ^{ 2 } = a ^{ 2 } + b ^{ 2 } − 2ab
(2 – 3) ^{ 2 } = 2 ^{ 2 } + 3 ^{ 2 } – 2(2)(3)
(–1) ^{ 2 } = 4 + 9 – 12
1 = 13 – 12
1 = 1
Identity III - a ^{ 2 } − b ^{ 2 } = (a − b) (a + b)
2 ^{ 2 } – 3 ^{ 2 } = (2 – 3) (2 + 3)
4 – 9 = – 1 × 5
–5 = –5
Identity IV - (x + a) (x + b) = x ^{ 2 } + (a + b) x + ab
(10 + 2) (10 + 3) = 10 ^{ 2 } + (2 + 3)10 + 2 × 3
12 × 13 = 100 + 5 × 10 + 6
156 = 100 + 50 + 6
156 = 156