What is expand (4x^{3/2}-2x^{1/2})^3 ?

The solution to expand (4x^{3/2}-2x^{1/2})^3 is 64x^{9/2}-96x^{7/2}+48x^{5/2}-8x^{3/2}

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expand (4x^{3/2}-2x^{1/2})^3

expand

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

64 x^{\frac{9}{2}} - 96 x^{\frac{7}{2}} + 48 x^{\frac{5}{2}} - 8 x^{\frac{3}{2}}

Solution steps

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

Apply Perfect Cube Formula:

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

(4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{3} = (4 x^{\frac{3}{2}})^{3} - 3 (4 x^{\frac{3}{2}})^{2} \cdot 2 x^{\frac{1}{2}} + 3 \cdot 4 x^{\frac{3}{2}} (2 x^{\frac{1}{2}})^{2} - (2 x^{\frac{1}{2}})^{3}

= (4 x^{\frac{3}{2}})^{3} - 3 (4 x^{\frac{3}{2}})^{2} \cdot 2 x^{\frac{1}{2}} + 3 \cdot 4 x^{\frac{3}{2}} (2 x^{\frac{1}{2}})^{2} - (2 x^{\frac{1}{2}})^{3}

(4 x^{\frac{3}{2}})^{3} = 64 x^{\frac{9}{2}}

3 (4 x^{\frac{3}{2}})^{2} \cdot 2 x^{\frac{1}{2}} = 96 x^{\frac{7}{2}}

3 \cdot 4 x^{\frac{3}{2}} (2 x^{\frac{1}{2}})^{2} = 48 x^{\frac{5}{2}}

(2 x^{\frac{1}{2}})^{3} = 8 x^{\frac{3}{2}}

= 64 x^{\frac{9}{2}} - 96 x^{\frac{7}{2}} + 48 x^{\frac{5}{2}} - 8 x^{\frac{3}{2}}

(x - 2 - 3) (x - 2 + 3)

(a - x)^{2}

(sec (θ) - tan (θ)) (csc (θ) + 1)

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

\frac{( s + 1 ) ^{3}}{s ^{4}}

What is expand (4x^{3/2}-2x^{1/2})^3 ?
The solution to expand (4x^{3/2}-2x^{1/2})^3 is 64x^{9/2}-96x^{7/2}+48x^{5/2}-8x^{3/2}