What is expand (x+sqrt(2))^5 ?

The solution to expand (x+sqrt(2))^5 is x^5+5sqrt(2)x^4+20x^3+20sqrt(2)x^2+20x+4sqrt(2)

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expand (x+sqrt(2))^5

expand

(x + 2)^{5}

x^{5} + 52 x^{4} + 20 x^{3} + 202 x^{2} + 20 x + 42

Solution steps

(x + 2)^{5}

Apply binomial theorem:

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

a = x, b = 2

= i = 0 \sum 5 (i 5) x^{(5 - i)} (2)^{i}

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (2)^{1} : 52 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (2)^{2} : 20 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (2)^{3} : 202 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (2)^{4} : 20 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (2)^{5} : 42

= x^{5} + 52 x^{4} + 20 x^{3} + 202 x^{2} + 20 x + 42

(t^{2} - 2 t) e^{1 - t^{3}}

(t - a) v (t^{'} - a)

\frac{d}{d t} ((x) (12 - 3 t^{3}))

\frac{3}{f ( x - 3 )}

\frac{m ( m + 5 ) + 4}{4 ( m + 5 ) ( m + 3 )}

What is expand (x+sqrt(2))^5 ?
The solution to expand (x+sqrt(2))^5 is x^5+5sqrt(2)x^4+20x^3+20sqrt(2)x^2+20x+4sqrt(2)