What is expand (sqrt(3)-x)^5 ?

The solution to expand (sqrt(3)-x)^5 is 9sqrt(3)-45x+30sqrt(3)x^2-30x^3+5sqrt(3)x^4-x^5

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expand (sqrt(3)-x)^5

expand

(3 - x)^{5}

93 - 45 x + 303 x^{2} - 30 x^{3} + 53 x^{4} - x^{5}

Solution steps

(3 - x)^{5}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 3, b = - x

= i = 0 \sum 5 (i 5) (3)^{(5 - i)} (- x)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (3)^{5} (- x)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (3)^{4} (- x)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (3)^{3} (- x)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (3)^{2} (- x)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (3)^{1} (- x)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (3)^{0} (- x)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3)^{5} (- x)^{0} : 93

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3)^{4} (- x)^{1} : - 45 x

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3)^{3} (- x)^{2} : 303 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3)^{2} (- x)^{3} : - 30 x^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3)^{1} (- x)^{4} : 53 x^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3)^{0} (- x)^{5} : - x^{5}

= 93 - 45 x + 303 x^{2} - 30 x^{3} + 53 x^{4} - x^{5}

\frac{d}{d t} ((x) (a t - a sin (t)))

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

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

\frac{\partial}{\partial z} ((x) (x z + x yz - 5))

(e^{2 x} - 6)^{2}

What is expand (sqrt(3)-x)^5 ?
The solution to expand (sqrt(3)-x)^5 is 9sqrt(3)-45x+30sqrt(3)x^2-30x^3+5sqrt(3)x^4-x^5