What is expand (sqrt(x)-9)^4 ?

The solution to expand (sqrt(x)-9)^4 is x^2-36xsqrt(x)+486x-2916sqrt(x)+6561

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expand (sqrt(x)-9)^4

expand

(x - 9)^{4}

x^{2} - 36 x x + 486 x - 2916 x + 6561

Solution steps

(x - 9)^{4}

Apply binomial theorem:

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

a = x, b = - 9

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} (- 9)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 9)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 9)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 9)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 9)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 9)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 9)^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 9)^{1} : - 36 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 9)^{2} : 486 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 9)^{3} : - 2916 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 9)^{4} : 6561

= x^{2} - 36 (x)^{3} + 486 x - 2916 x + 6561

Simplify

(x)^{3} : x x

= x^{2} - 36 x x + 486 x - 2916 x + 6561

(- 4) - 1

\frac{x ^{2} + 18 x + 81}{x ^{2} - 81}

54 x^{2} - 6 y^{2}

10 (- 1)

x^{2} - 2 x - 168

What is expand (sqrt(x)-9)^4 ?
The solution to expand (sqrt(x)-9)^4 is x^2-36xsqrt(x)+486x-2916sqrt(x)+6561