What is an Algebraic Identity?
An algebraic identity is an algebraic equation that is true for all values of the variables occurring in it.
Important Algebraic Identities:
(i) (x + y)2 = x2 + 2xy + y2
(ii) (x – y)2 = x2 – 2xy + y2
(iii) x2 – y2 = (x + y)(x – y)
(iv) (x + a)(x + b) = x2 + (a + b)x + ab
(v) (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(vi) (x + y)3 = x3 + y3 + 3xy(x + y)
(vii) (x – y)3 = x3 – y3 – 3xy(x – y)
(viii) x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz– zx)
(ix) If x + y + z = 0, then x3 + y3 + z3 = 3xyz
(x) x3 + y3 = (x + y)(x2 – xy + y2)
(xi) x3 – y3 = (x – y)(x2 + xy + y2)
