Basic Algebra/Solving Equations/Formulas

< Basic Algebra < Solving Equations

Basic Formulas

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

Derivation

$(a+b)^{2}<br/>=(a+b)(a+b)<br/>=a(a+b)+b(a+b)<br/>=a^{2}+ab+ab+b^{2}<br/>=a^{2}+2ab+b^{2}$

This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.