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

The solution to expand (3x-sqrt(3))^4 is 81x^4-108sqrt(3)x^3+162x^2-36sqrt(3)x+9

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expand (3x-sqrt(3))^4

expand

(3 x - 3)^{4}

81 x^{4} - 1083 x^{3} + 162 x^{2} - 363 x + 9

Solution steps

(3 x - 3)^{4}

Apply binomial theorem:

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

a = 3 x, b = - 3

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (- 3)^{1} : - 1083 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (- 3)^{2} : 162 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} (- 3)^{3} : - 363 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (- 3)^{4} : 9

= 81 x^{4} - 1083 x^{3} + 162 x^{2} - 363 x + 9

\frac{0.1 ( s + 1 ) ( s + 30.1 )}{s}

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

(\frac{3}{2}, \frac{5}{4}) y (\frac{1}{2}, - \frac{3}{4})

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

(sec (u) - tan (u)) (csc (u) + 1)

What is expand (3x-sqrt(3))^4 ?
The solution to expand (3x-sqrt(3))^4 is 81x^4-108sqrt(3)x^3+162x^2-36sqrt(3)x+9