What is expand (sqrt(x)+5)^4 ?

The solution to expand (sqrt(x)+5)^4 is x^2+20xsqrt(x)+150x+500sqrt(x)+625

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expand (sqrt(x)+5)^4

expand

(x + 5)^{4}

x^{2} + 20 x x + 150 x + 500 x + 625

Solution steps

(x + 5)^{4}

Apply binomial theorem:

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

a = x, b = 5

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} \cdot 5^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} \cdot 5^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} \cdot 5^{1} : 20 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} \cdot 5^{2} : 150 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} \cdot 5^{3} : 500 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} \cdot 5^{4} : 625

= x^{2} + 20 (x)^{3} + 150 x + 500 x + 625

Simplify

(x)^{3} : x x

= x^{2} + 20 x x + 150 x + 500 x + 625

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

(cos (β) - 1) (sin (β) - 1)

(s + 170) (s^{2} - 2025) (s + 20 π)

(2 + cos (2 θ))^{2}

(3 x + \frac{\frac{5}{6}}{x})^{8}

What is expand (sqrt(x)+5)^4 ?
The solution to expand (sqrt(x)+5)^4 is x^2+20xsqrt(x)+150x+500sqrt(x)+625