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Popular Álgebra >

expandir ((2α^2-αβ)/(β^2))^2

Solução

expandir

(\frac{2 α ^{2} - α β}{β ^{2}})^{2}

Solução

\frac{4 α ^{4}}{β ^{4}} - \frac{4 α ^{3}}{β ^{3}} + \frac{α ^{2}}{β ^{2}}

Passos da solução

(\frac{2 α ^{2} - α β}{β ^{2}})^{2}

Aplicar as propriedades dos expoentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 2 α ^{2} - α β ) ^{2}}{( β ^{2} ) ^{2}}

(β^{2})^{2} : β^{4}

= \frac{( 2 α ^{2} - α β ) ^{2}}{β ^{4}}

(2 α^{2} - α β)^{2} = 4 α^{4} - 4 α^{3} β + α^{2} β^{2}

= \frac{4 α ^{4} - 4 α ^{3} β + α ^{2} β ^{2}}{β ^{4}}

Aplicar as propriedades das frações:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4 α ^{4} - 4 α ^{3} β + α ^{2} β ^{2}}{β ^{4}} = \frac{4 α ^{4}}{β ^{4}} - \frac{4 α ^{3} β}{β ^{4}} + \frac{α ^{2} β ^{2}}{β ^{4}}

= \frac{4 α ^{4}}{β ^{4}} - \frac{4 α ^{3} β}{β ^{4}} + \frac{α ^{2} β ^{2}}{β ^{4}}

Cancelar

\frac{4 α ^{3} β}{β ^{4}} : \frac{4 α ^{3}}{β ^{3}}

= \frac{4 α ^{4}}{β ^{4}} - \frac{4 α ^{3}}{β ^{3}} + \frac{α ^{2} β ^{2}}{β ^{4}}

Cancelar

\frac{α ^{2} β ^{2}}{β ^{4}} : \frac{α ^{2}}{β ^{2}}

= \frac{4 α ^{4}}{β ^{4}} - \frac{4 α ^{3}}{β ^{3}} + \frac{α ^{2}}{β ^{2}}

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