What is expand ((2x^{1/2}-8)^3)/3 ?

The solution to expand ((2x^{1/2}-8)^3)/3 is (8x^{3/2})/3-32x+128x^{1/2}-512/3

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expand ((2x^{1/2}-8)^3)/3

expand

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

\frac{8 x ^{\frac{3}{2}}}{3} - 32 x + 128 x^{\frac{1}{2}} - \frac{512}{3}

Solution steps

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

(2 x^{\frac{1}{2}} - 8)^{3} = 8 x^{\frac{3}{2}} - 96 x + 384 x^{\frac{1}{2}} - 512

= \frac{8 x ^{\frac{3}{2}} - 96 x + 384 x ^{\frac{1}{2}} - 512}{3}

Apply the fraction rule:

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

\frac{8 x ^{\frac{3}{2}} - 96 x + 384 x ^{\frac{1}{2}} - 512}{3} = \frac{8 x ^{\frac{3}{2}}}{3} - \frac{96 x}{3} + \frac{384 x ^{\frac{1}{2}}}{3} - \frac{512}{3}

= \frac{8 x ^{\frac{3}{2}}}{3} - \frac{96 x}{3} + \frac{384 x ^{\frac{1}{2}}}{3} - \frac{512}{3}

Divide the numbers:

\frac{96}{3} = 32

= \frac{8 x ^{\frac{3}{2}}}{3} - 32 x + \frac{384 x ^{\frac{1}{2}}}{3} - \frac{512}{3}

Divide the numbers:

\frac{384}{3} = 128

= \frac{8 x ^{\frac{3}{2}}}{3} - 32 x + 128 x^{\frac{1}{2}} - \frac{512}{3}

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

C e^{2 x} + \frac{1}{4} (2 x^{2} + 2 x + 1)

(3 - a)^{2}

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

(7 + e^{- 3 t})^{2}

What is expand ((2x^{1/2}-8)^3)/3 ?
The solution to expand ((2x^{1/2}-8)^3)/3 is (8x^{3/2})/3-32x+128x^{1/2}-512/3