## Important Algebraic Expressions and Identities

**(a + b) ^{2} = a^{2} + b^{2} + 2ab**

**(a – b) ^{2} = a^{2} + b^{2} – 2ab**

**a ^{2} – b^{2} = (a + b)(a – b)**

**(a + b) ^{2} = (a – b)^{2} + 4ab**

**(a – b) ^{2} = (a + b)^{2} – 4ab**

**(x + a)(x + b) = x ^{2} +( a + b)x + ab**

**a ^{3} + b^{3} = (a + b) (a^{2} + b^{2} – ab)**

**a ^{3} – b^{3} = (a – b) (a^{2} + b^{2} + ab)**

**(a + b) ^{3} = a^{3} + b^{3} + 3a^{2}b + 3ab^{2}**

**(a – b) ^{3} = a^{3} – b^{3} – 3a^{2}b + 3ab^{2}**

**a ^{3} + b^{3} = (a + b)^{3} – 3ab (a + b)**

**a ^{3} – b^{3} = (a – b)^{3} + 3ab (a – b)**

**(a + b) ^{3} = a^{3} + b^{3} + 3ab(a + b)**

**(a – b) ^{3} = a^{3} – b^{3} – 3ab(a – b)**

**a ^{3} + b^{3} + c^{3} -3abc = (a + b + c)( a^{2} + b^{2} + c^{2} – ab –bc – ca)**

**a ^{3} + b^{3} + c^{3} -3abc = (a + b + c) ½ (2a^{2} +2 b^{2} +2 c^{2} – 2ab –2bc – 2ca)**

**a ^{3} + b^{3} + c^{3} -3abc = ½ (a + b + c)[(a – b)^{2} +(b- c)^{2} + (c – a)^{2}]**

**If a + b + c = 0, then a ^{3} + b^{3} + c^{3} = 3abc**

**(a + b + c) ^{3 }= a^{3} + b^{3} + c^{3} + 3(a + b)(b + c)(c + a)**

**a ^{2} + b^{2} = (a + b)^{2} – 2ab**

**a ^{2} + b^{2} = (a – b)^{2} + 2ab**

**(a + b + c) ^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca**

**a ^{4} + b^{4} a^{2}b^{2} = (a^{2} – ab + b^{2}) (a^{2} + b^{2} + ab)**