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# Describe Law of Identity

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## Law of Identity in MathematicsAn identity in mathematics is a relationship between two mathematical expressions A and B such that A and B generate the same value for all values of the variables within a specified range of validity.According to the law of identity, if a statement has been determined to be true, it is true.Boolean LawsBoolean algebra is the category of algebra in which the variable’s values are the truth values, true and false, ordinary denoted 1 and 0 respectively.Boolean Algebra OperationsThe basic operations of Boolean algebra are as follows:Conjunction or AND operationDisjunction or OR operationNegation or Not operationAlgebraic IdentitiesThe algebraic equations which are valid for all values of variables in them are called algebraic identities.Standard Algebraic Identities ListAll the standard Algebraic Identities are derived from the Binomial Theorem, which is given as:${\left(a+b\right)}^{n}={C}_{0}^{n}.{a}^{n}.{b}^{0}+{C}_{1}^{n}.{a}^{n-1}.{b}^{1}+\dots \dots ..+{C}_{n-1}^{n}.{a}^{1}.{b}^{n-1}+{C}_{n}^{n}.{a}^{0}.{b}^{n}$Some Standard Algebraic Identities list are given below:Identity I: ${\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}$Identity II: ${\left(a–b\right)}^{2}={a}^{2}–2ab+{b}^{2}$Identity III: ${a}^{2}–{b}^{2}=\left(a+b\right)\left(a–b\right)$Identity IV:$\left(x+a\right)\left(x+b\right)={x}^{2}+\left(a+b\right)x+ab$Identity V: ${\left(a+b+c\right)}^{2}={a}^{2}+{b}^{2}+{c}^{2}+2ab+2bc+2ca$Identity VI: ${\left(a+b\right)}^{3}={a}^{3}+{b}^{3}+3ab\left(a+b\right)$Identity VII: ${\left(a–b\right)}^{3}={a}^{3}–{b}^{3}–3ab\left(a–b\right)$Identity VIII: ${a}^{3}+{b}^{3}+{c}^{3}–3abc=\left(a+b+c\right)\left({a}^{2}+{b}^{2}+{c}^{2}–ab–bc–ca\right)$Hence proved.

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