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

The solution to expand (sqrt(x)-4)^4 is x^2-16xsqrt(x)+96x-256sqrt(x)+256

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expand (sqrt(x)-4)^4

expand

(x - 4)^{4}

x^{2} - 16 x x + 96 x - 256 x + 256

Solution steps

(x - 4)^{4}

Apply binomial theorem:

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

a = x, b = - 4

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 4)^{1} : - 16 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 4)^{2} : 96 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 4)^{3} : - 256 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 4)^{4} : 256

= x^{2} - 16 (x)^{3} + 96 x - 256 x + 256

Simplify

(x)^{3} : x x

= x^{2} - 16 x x + 96 x - 256 x + 256

0.03 \cdot 1 (1. 2^{1})

(5 x^{2} - 4) (5 w^{2} - \frac{3}{2})

(x - 7) (x - 6)^{8} ln (\frac{x}{5})

\frac{3 ( y - x \frac{d y}{d x} )}{5 y ^{2}}

(x - 4)^{3}

What is expand (sqrt(x)-4)^4 ?
The solution to expand (sqrt(x)-4)^4 is x^2-16xsqrt(x)+96x-256sqrt(x)+256