Algebraic Identities

The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are used for the factorization of polynomials. Algebraic identities are used in the computation of algebraic expressions and solving different polynomials.

Some Standard Algebraic Identities list are given below:

Identity I: $(a+b)^{2}=a^{2}+2ab+b^{2}$

Identity II: $(a-b)^{2}=a^{2}-2ab+b^{2}$

Identity III: $a^{2}-b^{2}=(a+b)(a-b)$

Identity IV: $(x+a)(x+b)=x^{2}+(a+b)x+ab$

Identity V: $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$

Identity VI: $(a+b)^{3}=a^{3}+b^{3}+3ab(a+b)$

Identity VII: $(a-b)^{3}=a^{3}-b^{3}-3ab(a-b)$

Identity VIII: $a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$