What is expand ((3x+2y)^3)/x ?

The solution to expand ((3x+2y)^3)/x is 27x^2+54xy+36y^2+(8y^3)/x

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expand ((3x+2y)^3)/x

expand

\frac{( 3 x + 2 y ) ^{3}}{x}

27 x^{2} + 54 x y + 36 y^{2} + \frac{8 y ^{3}}{x}

Solution steps

\frac{( 3 x + 2 y ) ^{3}}{x}

(3 x + 2 y)^{3} = 27 x^{3} + 54 x^{2} y + 36 x y^{2} + 8 y^{3}

= \frac{27 x ^{3} + 54 x ^{2} y + 36 x y ^{2} + 8 y ^{3}}{x}

Apply the fraction rule:

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

\frac{27 x ^{3} + 54 x ^{2} y + 36 x y ^{2} + 8 y ^{3}}{x} = \frac{27 x ^{3}}{x} + \frac{54 x ^{2} y}{x} + \frac{36 x y ^{2}}{x} + \frac{8 y ^{3}}{x}

= \frac{27 x ^{3}}{x} + \frac{54 x ^{2} y}{x} + \frac{36 x y ^{2}}{x} + \frac{8 y ^{3}}{x}

Cancel

\frac{27 x ^{3}}{x} : 27 x^{2}

= 27 x^{2} + \frac{54 x ^{2} y}{x} + \frac{36 x y ^{2}}{x} + \frac{8 y ^{3}}{x}

Cancel

\frac{54 x ^{2} y}{x} : 54 x y

= 27 x^{2} + 54 x y + \frac{36 x y ^{2}}{x} + \frac{8 y ^{3}}{x}

Cancel

\frac{36 x y ^{2}}{x} : 36 y^{2}

= 27 x^{2} + 54 x y + 36 y^{2} + \frac{8 y ^{3}}{x}

\frac{( - 3 x - 8 ) ( x - 1 )}{9}

\frac{( x ^{2} - 9 ) ( x - 2 )}{3 x + 6}

\frac{2 A - 3}{2 ( A - 1 )}

L im x \Rightarrow 3 (2 x - 3)

[(3 ab + 5 c d)^{2}] [(4 e f - 6 g h)^{2}]

What is expand ((3x+2y)^3)/x ?
The solution to expand ((3x+2y)^3)/x is 27x^2+54xy+36y^2+(8y^3)/x