What is expand (sqrt(x)-6)^4 ?

The solution to expand (sqrt(x)-6)^4 is x^2-24xsqrt(x)+216x-864sqrt(x)+1296

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expand (sqrt(x)-6)^4

expand

(x - 6)^{4}

x^{2} - 24 x x + 216 x - 864 x + 1296

Solution steps

(x - 6)^{4}

Apply binomial theorem:

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

a = x, b = - 6

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} (- 6)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 6)^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 6)^{1} : - 24 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 6)^{2} : 216 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 6)^{3} : - 864 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 6)^{4} : 1296

= x^{2} - 24 (x)^{3} + 216 x - 864 x + 1296

Simplify

(x)^{3} : x x

= x^{2} - 24 x x + 216 x - 864 x + 1296

10 (y + 5 x) e^{y + 5 x} + e^{y + 5 x} \cdot 5 (y + 5 x)^{2}

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

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

\frac{1}{s ^{4} ( s - 5 )}

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

What is expand (sqrt(x)-6)^4 ?
The solution to expand (sqrt(x)-6)^4 is x^2-24xsqrt(x)+216x-864sqrt(x)+1296