Important Algebraic Expressions and Identities

(a + b)2 = a2 + b2 + 2ab

(a – b)2 = a2 + b2 – 2ab

a2 – b2 = (a + b)(a – b)

(a + b)2 = (a – b)2  + 4ab

(a – b)2 = (a + b)2 – 4ab

(x + a)(x + b) = x2 +( a + b)x + ab

a3 + b3 = (a + b) (a2 + b2 – ab)

a3 – b3 = (a – b) (a2 + b2 + ab)

(a + b)3 = a3 + b3 + 3a2b + 3ab2

(a – b)3 = a3 – b3 – 3a2b + 3ab2

a3 + b3 = (a + b)3 – 3ab (a + b)

a3 – b3 = (a – b)3 + 3ab (a – b)

(a + b)3 = a3 + b3 + 3ab(a + b)

(a – b)3 = a3 – b3 – 3ab(a – b)

a3 + b3 + c3 -3abc = (a + b + c)( a2 + b2 + c2 – ab –bc – ca)

a3 + b3 + c3 -3abc = (a + b + c) ½ (2a2 +2 b2 +2 c2 – 2ab –2bc – 2ca)

a3 + b3 + c3 -3abc = ½ (a + b + c)[(a – b)2 +(b- c)2 + (c – a)2]

If a + b + c = 0, then a3 + b3 + c3 = 3abc

(a + b + c)3 = a3 + b3 + c3 + 3(a + b)(b + c)(c + a)

a2 + b2 = (a + b)2 – 2ab

a2 + b2 = (a – b)2 + 2ab

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

a4 + b4 a2b2 = (a2 – ab + b2) (a2 + b2 + ab)