What is expand (sqrt(6)+x)^6 ?

The solution to expand (sqrt(6)+x)^6 is 216+216sqrt(6)x+540x^2+120sqrt(6)x^3+90x^4+6sqrt(6)x^5+x^6

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expand (sqrt(6)+x)^6

expand

(6 + x)^{6}

216 + 2166 x + 540 x^{2} + 1206 x^{3} + 90 x^{4} + 66 x^{5} + x^{6}

Solution steps

(6 + x)^{6}

Apply binomial theorem:

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

a = 6, b = x

= i = 0 \sum 6 (i 6) (6)^{(6 - i)} x^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} (6)^{6} x^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (6)^{5} x^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (6)^{4} x^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (6)^{3} x^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (6)^{2} x^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (6)^{1} x^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (6)^{0} x^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (6)^{6} x^{0} : 216

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (6)^{5} x^{1} : 2166 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (6)^{4} x^{2} : 540 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (6)^{3} x^{3} : 1206 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (6)^{2} x^{4} : 90 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (6)^{1} x^{5} : 66 x^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (6)^{0} x^{6} : x^{6}

= 216 + 2166 x + 540 x^{2} + 1206 x^{3} + 90 x^{4} + 66 x^{5} + x^{6}

t e (x^{3} y (t, x) - y (t, x) (t, x)^{2} = 3)

\frac{( x - 8 ) ( x - 2 )}{( x + 6 ) ( x - 3 )}

(1 + 0.024)^{X}

(5 x + (- 9) y = - 5) (0)

\frac{x y ( 1 - z )}{e ^{z}}

What is expand (sqrt(6)+x)^6 ?
The solution to expand (sqrt(6)+x)^6 is 216+216sqrt(6)x+540x^2+120sqrt(6)x^3+90x^4+6sqrt(6)x^5+x^6