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

The solution to expand (x^{3/2}-x+1)(x^2+x^{1/2}-2) is -x^3+2x^2+x^{7/2}-3x^{3/2}+x^{1/2}+2x-2

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

expand

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

- x^{3} + 2 x^{2} + x^{\frac{7}{2}} - 3 x^{\frac{3}{2}} + x^{\frac{1}{2}} + 2 x - 2

Solution steps

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

Distribute parentheses

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

Simplify

x^{\frac{3}{2}} x^{2} + x^{\frac{3}{2}} x^{\frac{1}{2}} + x^{\frac{3}{2}} (- 2) - x x^{2} - x x^{\frac{1}{2}} - x (- 2) + 1 \cdot x^{2} + 1 \cdot x^{\frac{1}{2}} + 1 \cdot (- 2) : - x^{3} + 2 x^{2} + x^{\frac{7}{2}} - 3 x^{\frac{3}{2}} + x^{\frac{1}{2}} + 2 x - 2

= - x^{3} + 2 x^{2} + x^{\frac{7}{2}} - 3 x^{\frac{3}{2}} + x^{\frac{1}{2}} + 2 x - 2

\frac{5 x ^{3} + 4 x ^{2} + 7 x + 3}{( x ^{2} + 2 x + 2 ) ( x ^{2} - x - 1 )}

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

(2 x^{2} + 3 x) (x - 1)

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

What is expand (x^{3/2}-x+1)(x^2+x^{1/2}-2) ?
The solution to expand (x^{3/2}-x+1)(x^2+x^{1/2}-2) is -x^3+2x^2+x^{7/2}-3x^{3/2}+x^{1/2}+2x-2