List of all Algebraic Identities and Conditional Identity

Algebraic Identities

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

$(ii){{(a-b)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab $

$(iii)({{a}^{2}}-{{b}^{2}})=(a-b)(a+b)$

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

$(v)(x-a)(x+b)={{x}^{2}}+(b-a)x-ab $

$(vi)(x+a)(x-b)={{x}^{2}}+(a-b)x-ab $

$(vii)(x-a)(x-b)={{x}^{2}}-(a+b)x+ab $

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

$(ix){{(a+b-c)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2ab-2bc-2ca $

$(x){{(a-b+c)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}-2ab-2bc+2ca $

$(xi){{(a-b-c)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}-2ab+2bc-2ca$

$(xii){{a}^{3}}+{{b}^{3}}=(a+b)({{a}^{2}}-ab+{{b}^{2}}) $

$(xiii){{a}^{3}}-{{b}^{3}}=(a-b)({{a}^{2}}+ab+{{b}^{2}}) $

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

$(xv){{(a-b)}^{3}}={{a}^{3}}-{{b}^{3}}-3ab(a-b)={{a}^{3}}-{{b}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}$

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

Conditional Identity

(xvii) If a+b+c=0, then
    ${{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc$

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