**Mathematics > Expansion > Formula**

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

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

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

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

**(v) a**^{2 }– b^{2}= (a+b)(a-b).

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

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

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

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

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

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

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

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