What is expand (t^{1/2}x+t^{1/3}y)^3 ?

The solution to expand (t^{1/2}x+t^{1/3}y)^3 is t^{3/2}x^3+3t^{4/3}x^2y+3t^{7/6}xy^2+ty^3

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expand (t^{1/2}x+t^{1/3}y)^3

expand

(t^{\frac{1}{2}} x + t^{\frac{1}{3}} y)^{3}

t^{\frac{3}{2}} x^{3} + 3 t^{\frac{4}{3}} x^{2} y + 3 t^{\frac{7}{6}} x y^{2} + t y^{3}

Solution steps

(t^{\frac{1}{2}} x + t^{\frac{1}{3}} y)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(t^{\frac{1}{2}} x + t^{\frac{1}{3}} y)^{3} = (t^{\frac{1}{2}} x)^{3} + 3 (t^{\frac{1}{2}} x)^{2} t^{\frac{1}{3}} y + 3 t^{\frac{1}{2}} x (t^{\frac{1}{3}} y)^{2} + (t^{\frac{1}{3}} y)^{3}

= (t^{\frac{1}{2}} x)^{3} + 3 (t^{\frac{1}{2}} x)^{2} t^{\frac{1}{3}} y + 3 t^{\frac{1}{2}} x (t^{\frac{1}{3}} y)^{2} + (t^{\frac{1}{3}} y)^{3}

(t^{\frac{1}{2}} x)^{3} = t^{\frac{3}{2}} x^{3}

3 (t^{\frac{1}{2}} x)^{2} t^{\frac{1}{3}} y = 3 t^{\frac{4}{3}} x^{2} y

3 t^{\frac{1}{2}} x (t^{\frac{1}{3}} y)^{2} = 3 t^{\frac{7}{6}} x y^{2}

(t^{\frac{1}{3}} y)^{3} = t y^{3}

= t^{\frac{3}{2}} x^{3} + 3 t^{\frac{4}{3}} x^{2} y + 3 t^{\frac{7}{6}} x y^{2} + t y^{3}

\frac{( 1 - \frac{1}{x ^{3} + 2} )}{( x + \frac{1}{x - 1} )}

(x - 1 + i 2)^{2} \cdot (x + 1 + i 2)^{2}

lo g_{x} (\frac{y}{3 z})

(x - 5) (x + 5)

x^{2} (1 + 1 - x^{2})

What is expand (t^{1/2}x+t^{1/3}y)^3 ?
The solution to expand (t^{1/2}x+t^{1/3}y)^3 is t^{3/2}x^3+3t^{4/3}x^2y+3t^{7/6}xy^2+ty^3