What is expand (sqrt(2)+sqrt(5))^4 ?

The solution to expand (sqrt(2)+sqrt(5))^4 is 89+28sqrt(10)

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expand (sqrt(2)+sqrt(5))^4

expand

(2 + 5)^{4}

89 + 2810

Solution steps

(2 + 5)^{4}

Apply binomial theorem:

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

a = 2, b = 5

= i = 0 \sum 4 (i 4) (2)^{(4 - i)} (5)^{i}

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2)^{3} (5)^{1} : 810

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2)^{2} (5)^{2} : 60

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2)^{1} (5)^{3} : 2010

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2)^{0} (5)^{4} : 25

= 4 + 810 + 60 + 2010 + 25

4 + 810 + 60 + 2010 + 25 = 89 + 2810

= 89 + 2810

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What is expand (sqrt(2)+sqrt(5))^4 ?
The solution to expand (sqrt(2)+sqrt(5))^4 is 89+28sqrt(10)