What is expand (sqrt(x)-2)^6 ?

The solution to expand (sqrt(x)-2)^6 is x^3-12x^2sqrt(x)+60x^2-160xsqrt(x)+240x-192sqrt(x)+64

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expand (sqrt(x)-2)^6

expand

(x - 2)^{6}

x^{3} - 12 x^{2} x + 60 x^{2} - 160 x x + 240 x - 192 x + 64

Solution steps

(x - 2)^{6}

Apply binomial theorem:

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

a = x, b = - 2

= i = 0 \sum 6 (i 6) (x)^{(6 - i)} (- 2)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (x)^{6} (- 2)^{0} : x^{3}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (x)^{5} (- 2)^{1} : - 12 (x)^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (x)^{4} (- 2)^{2} : 60 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (x)^{3} (- 2)^{3} : - 160 (x)^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (x)^{2} (- 2)^{4} : 240 x

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (x)^{1} (- 2)^{5} : - 192 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (x)^{0} (- 2)^{6} : 64

= x^{3} - 12 (x)^{5} + 60 x^{2} - 160 (x)^{3} + 240 x - 192 x + 64

(x)^{5} = x^{2} x

(x)^{3} = x x

= x^{3} - 12 x^{2} x + 60 x^{2} - 160 x x + 240 x - 192 x + 64

arcsin (\frac{1}{3} \cdot (x - 2))

- \frac{5 ( 13 - X )}{2}

(t sin (t^{2})) (2 t^{2} cos (t^{2}) + sin (t^{2}))

\frac{π ( 63 t + 22 )}{9 t ^{2} + 12 t + 4}

(cos^{2} (x) - 2 sin (x))^{2}

What is expand (sqrt(x)-2)^6 ?
The solution to expand (sqrt(x)-2)^6 is x^3-12x^2sqrt(x)+60x^2-160xsqrt(x)+240x-192sqrt(x)+64