Identities I to IV

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