The algebraic equations which are valid for all values of variables in them are called algebraic identities
Algebraic identities are helpful in factorizing polynomial and come handy when solving polymonial functions and expressions.
Expression |
Value |
| (a+b)2 | a2 + 2ab + b2 |
| (a – b)2 | a2 – 2ab + b2 |
| (a – b)*(a+b) | a2 – b2 |
| (a + b)3 | a3 + 3a2 b + 3ab2+ b3 |
| (a – b)3 | a3 – 3a2 b + 3ab2 – b3 |
| a3 + b3 | (a+b) (a2 – ab + b2) |
| a3 – b3 | (a-b) (a2 + ab + b2) |
| (a + b +c)2 | a2 + b2 + c2 + 2ab + 2bc + 2ca |
| (a + b +c)3 | a3 + b3 + c3 + 3(a+b)(b+c)(c+a) |
| a3 + b3 + c3 – 3abc | (a + b + c) (a2 + b2 + c2 -ab – bc – ca)
or ½*(a + b + c) [(a-b)2 + (b-c)2 + (c-a)2] |
| If a + b + c = 0; then a3 + b3 + c3 = |
3abc |