What is factor x^{3/2}-8 ?

The solution to factor x^{3/2}-8 is (sqrt(x)-2)(x+2sqrt(x)+4)

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factor x^{3/2}-8

factor

x^{\frac{3}{2}} - 8

(x - 2) (x + 2 x + 4)

Solution steps

x^{\frac{3}{2}} - 8

Rewrite

x^{\frac{3}{2}}

(x)^{3}

= (x)^{3} - 8

Rewrite

8

2^{3}

= (x)^{3} - 2^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(x)^{3} - 2^{3} = (x - 2) ((x)^{2} + 2 x + 2^{2})

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

Refine

= (x - 2) ((x)^{2} + 2 x + 4)

Simplify

(x - 2) ((x)^{2} + 2 x + 4) : (x - 2) (x + 2 x + 4)

= (x - 2) (x + 2 x + 4)

x^{2} - x - 4

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

10 0^{2} 1

COM U N^{4} (X - 3) 5 (X - 3)

- 2 x + 3 x

What is factor x^{3/2}-8 ?
The solution to factor x^{3/2}-8 is (sqrt(x)-2)(x+2sqrt(x)+4)