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

The solution to expand x^{1/2}*(x^2+1) is x^{5/2}+x^{1/2}

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expand x^{1/2}*(x^2+1)

expand

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

x^{\frac{5}{2}} + x^{\frac{1}{2}}

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

= x^{\frac{1}{2}} x^{2} + x^{\frac{1}{2}} \cdot 1

x^{\frac{1}{2}} x^{2} = x^{\frac{5}{2}}

x^{\frac{1}{2}} \cdot 1 = x^{\frac{1}{2}}

= x^{\frac{5}{2}} + x^{\frac{1}{2}}

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

\frac{( z ( 1 + 2 z ^{2} ) )}{( ( - 2 + z ) ^{2} ( - 1 + z ) )}

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

(1, - 2) y (1, - 4)

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

What is expand x^{1/2}*(x^2+1) ?
The solution to expand x^{1/2}*(x^2+1) is x^{5/2}+x^{1/2}