What is expand (sqrt(x)+1)(sqrt(x)-1)^5 ?

The solution to expand (sqrt(x)+1)(sqrt(x)-1)^5 is x^3-4x^2sqrt(x)+5x^2-5x+4sqrt(x)-1

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expand (sqrt(x)+1)(sqrt(x)-1)^5

expand

(x + 1) (x - 1)^{5}

x^{3} - 4 x^{2} x + 5 x^{2} - 5 x + 4 x - 1

Solution steps

(x + 1) (x - 1)^{5}

= (x - 1)^{5} (x + 1)

Apply the distributive law:

a (b + c) = ab + a c

(x - 1)^{5} (x + 1) = (x - 1)^{5} x + (x - 1)^{5} \cdot 1

= (x - 1)^{5} x + (x - 1)^{5} \cdot 1

Simplify

(x - 1)^{5} x + (x - 1)^{5} \cdot 1 : x (x - 1)^{5} + (x - 1)^{5}

= x (x - 1)^{5} + (x - 1)^{5}

Expand

x (x - 1)^{5} : x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x

= x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x + (x - 1)^{5}

Expand

(x - 1)^{5} : (x)^{5} - 5 x^{2} + 10 (x)^{3} - 10 x + 5 x - 1

= x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x + (x)^{5} - 5 x^{2} + 10 (x)^{3} - 10 x + 5 x - 1

Simplify

x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x + (x)^{5} - 5 x^{2} + 10 (x)^{3} - 10 x + 5 x - 1 : x^{3} - 4 x^{2} x + 5 x^{2} - 5 x + 4 x - 1

= x^{3} - 4 x^{2} x + 5 x^{2} - 5 x + 4 x - 1

\frac{x}{( 1 - 4 x ) ^{2}}

\frac{( 2 s ^{3} - s ^{2} )}{( 4 s ^{2} - 4 s + 5 ) ^{2}}

(x - 2 + 3) (x - 2 - 3)

(1 - \frac{x}{4})^{10}

(6 - 2 x^{\frac{1}{2}})^{2}

What is expand (sqrt(x)+1)(sqrt(x)-1)^5 ?
The solution to expand (sqrt(x)+1)(sqrt(x)-1)^5 is x^3-4x^2sqrt(x)+5x^2-5x+4sqrt(x)-1