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

The solution to expand (4x^{3/2}-2x^{1/2})^2 is 16x^3-16x^2+4x

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

expand

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

16 x^{3} - 16 x^{2} + 4 x

Solution steps

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

Apply Perfect Square Formula:

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

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

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

(4 x^{\frac{3}{2}})^{2} = 16 x^{3}

2 \cdot 4 x^{\frac{3}{2}} \cdot 2 x^{\frac{1}{2}} = 16 x^{2}

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

= 16 x^{3} - 16 x^{2} + 4 x

\frac{- 2 s ^{2} - 6}{( s ^{2} + 4 ) ( s ^{2} - 4 )}

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

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

0.03916 (1 - e^{(- 2.3 t)}) - 0.015 t

2 (7 i + 8 j) - 3 (8 + \frac{5 π}{6})

What is expand (4x^{3/2}-2x^{1/2})^2 ?
The solution to expand (4x^{3/2}-2x^{1/2})^2 is 16x^3-16x^2+4x