Factorization, sometimes also known as factoring consists of writing a number or another mathematical object as a product of several factors. Usually, factors are smaller or simpler objects of the same kind.
Algebraic Identities: An algebraic identity is an algebraic equation that is true for all values of the variable occurring in it.
Some algebraic identities are given below
- (x + y)2 = x2 + 2xy + y2
- (x – y)2 = x2 – 2xy + y2
- x2 – y2 = (x + y)(x – y)
- (x + a)(x + b)= x2 + (a + b)x + ab
- (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
- (x + y)3 = x3 + y3 + 3xy(x + y)
- (x – y)3 = x3 – y3 – 3xy(x – y)
- x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx)
If x + y + z = 0, then x3 + y3 + z3 = 3xyz