What is expand (sqrt(x)-7)^4 ?

The solution to expand (sqrt(x)-7)^4 is x^2-28xsqrt(x)+294x-1372sqrt(x)+2401

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expand (sqrt(x)-7)^4

expand

(x - 7)^{4}

x^{2} - 28 x x + 294 x - 1372 x + 2401

Solution steps

(x - 7)^{4}

Apply binomial theorem:

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

a = x, b = - 7

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} (- 7)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 7)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 7)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 7)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 7)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 7)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 7)^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 7)^{1} : - 28 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 7)^{2} : 294 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 7)^{3} : - 1372 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 7)^{4} : 2401

= x^{2} - 28 (x)^{3} + 294 x - 1372 x + 2401

Simplify

(x)^{3} : x x

= x^{2} - 28 x x + 294 x - 1372 x + 2401

- \frac{1}{3} (\frac{L}{3} - 0.4)^{3}

(3 + 5) (3 + 1) (3 - 5) (3 - 1)

cos (x) (x - 1)

\frac{( 2 s + 1 ) e ^{- 4 s}}{4 s ^{2} + 4 s + 5}

What is expand (sqrt(x)-7)^4 ?
The solution to expand (sqrt(x)-7)^4 is x^2-28xsqrt(x)+294x-1372sqrt(x)+2401