What is (4x^3+6/(x^3))(x^{3/2}-4x) ?

The solution to (4x^3+6/(x^3))(x^{3/2}-4x) is ((4x^6+6)(x^{3/2}-4x))/(x^3)

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simplify (4x^3+6/(x^3))(x^{3/2}-4x)

simplify

(4 x^{3} + \frac{6}{x ^{3}}) (x^{\frac{3}{2}} - 4 x)

\frac{( 4 x ^{6} + 6 ) ( x ^{\frac{3}{2}} - 4 x )}{x ^{3}}

Solution steps

(4 x^{3} + \frac{6}{x ^{3}}) (x^{\frac{3}{2}} - 4 x)

Join

4 x^{3} + \frac{6}{x ^{3}} : \frac{4 x ^{6} + 6}{x ^{3}}

= \frac{4 x ^{6} + 6}{x ^{3}} (x^{\frac{3}{2}} - 4 x)

Apply the fraction rule:

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

= \frac{( 4 x ^{6} + 6 ) ( x ^{\frac{3}{2}} - 4 x )}{x ^{3}}

(x - 1) (2 x + 5)

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

(2 + \frac{t}{2})^{7}

(2 + 3) (3 - 2)

\frac{2 x + 4 x e ^{3 x} - 6 x ^{2} e ^{3 x}}{( 1 + 2 e ^{3 x} ) ^{2}}

What is (4x^3+6/(x^3))(x^{3/2}-4x) ?
The solution to (4x^3+6/(x^3))(x^{3/2}-4x) is ((4x^6+6)(x^{3/2}-4x))/(x^3)