What is expand (-7x-3x^{1/2})^3 ?

The solution to expand (-7x-3x^{1/2})^3 is -343x^3-441x^{5/2}-189x^2-27x^{3/2}

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expand (-7x-3x^{1/2})^3

expand

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

- 343 x^{3} - 441 x^{\frac{5}{2}} - 189 x^{2} - 27 x^{\frac{3}{2}}

Solution steps

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

Apply Perfect Cube Formula:

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

(- 7 x - 3 x^{\frac{1}{2}})^{3} = (- 7 x)^{3} - 3 (- 7 x)^{2} \cdot 3 x^{\frac{1}{2}} + 3 (- 7 x) (3 x^{\frac{1}{2}})^{2} - (3 x^{\frac{1}{2}})^{3}

= (- 7 x)^{3} - 3 (- 7 x)^{2} \cdot 3 x^{\frac{1}{2}} + 3 (- 7 x) (3 x^{\frac{1}{2}})^{2} - (3 x^{\frac{1}{2}})^{3}

(- 7 x)^{3} = - 343 x^{3}

3 (- 7 x)^{2} \cdot 3 x^{\frac{1}{2}} = 441 x^{\frac{5}{2}}

3 (- 7 x) (3 x^{\frac{1}{2}})^{2} = - 189 x^{2}

(3 x^{\frac{1}{2}})^{3} = 27 x^{\frac{3}{2}}

= - 343 x^{3} - 441 x^{\frac{5}{2}} - 189 x^{2} - 27 x^{\frac{3}{2}}

(- 3) \cdot (\frac{- b}{6})^{2} - b \cdot (\frac{- b}{6})

m^{6} + 125

(x^{4})^{2} \cdot x^{- 3}

9 x^{2} + 36 x y + 36 y^{2}

50 x^{3} y^{2} - 98 x y^{4}

What is expand (-7x-3x^{1/2})^3 ?
The solution to expand (-7x-3x^{1/2})^3 is -343x^3-441x^{5/2}-189x^2-27x^{3/2}