What is expand (sqrt(x)-3)^4 ?

The solution to expand (sqrt(x)-3)^4 is x^2-12xsqrt(x)+54x-108sqrt(x)+81

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expand (sqrt(x)-3)^4

expand

(x - 3)^{4}

x^{2} - 12 x x + 54 x - 108 x + 81

Solution steps

(x - 3)^{4}

Apply binomial theorem:

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

a = x, b = - 3

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 3)^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 3)^{1} : - 12 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 3)^{2} : 54 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 3)^{3} : - 108 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 3)^{4} : 81

= x^{2} - 12 (x)^{3} + 54 x - 108 x + 81

Simplify

(x)^{3} : x x

= x^{2} - 12 x x + 54 x - 108 x + 81

(1 + \frac{x}{2})^{14}

(x - y) (x + y)

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

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

(e^{3 x} + e^{- 3 x}) (e^{3 x} - e^{- 3 x})

What is expand (sqrt(x)-3)^4 ?
The solution to expand (sqrt(x)-3)^4 is x^2-12xsqrt(x)+54x-108sqrt(x)+81