What is expand (a(a^5-ab^2+b^3))/b ?

The solution to expand (a(a^5-ab^2+b^3))/b is (a^6)/b-a^2b+ab^2

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expand (a(a^5-ab^2+b^3))/b

expand

\frac{a ( a ^{5} - a b ^{2} + b ^{3} )}{b}

\frac{a ^{6}}{b} - a^{2} b + a b^{2}

Solution steps

\frac{a ( a ^{5} - a b ^{2} + b ^{3} )}{b}

Expand

a (a^{5} - a b^{2} + b^{3}) : a^{6} - a^{2} b^{2} + a b^{3}

= \frac{a ^{6} - a ^{2} b ^{2} + a b ^{3}}{b}

Apply the fraction rule:

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

\frac{a ^{6} - a ^{2} b ^{2} + a b ^{3}}{b} = \frac{a ^{6}}{b} - \frac{a ^{2} b ^{2}}{b} + \frac{a b ^{3}}{b}

= \frac{a ^{6}}{b} - \frac{a ^{2} b ^{2}}{b} + \frac{a b ^{3}}{b}

Cancel

\frac{a ^{2} b ^{2}}{b} : a^{2} b

= \frac{a ^{6}}{b} - a^{2} b + \frac{a b ^{3}}{b}

Cancel

\frac{a b ^{3}}{b} : a b^{2}

= \frac{a ^{6}}{b} - a^{2} b + a b^{2}

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What is expand (a(a^5-ab^2+b^3))/b ?
The solution to expand (a(a^5-ab^2+b^3))/b is (a^6)/b-a^2b+ab^2