What is expand (sqrt(2)+sqrt(3))^4 ?

The solution to expand (sqrt(2)+sqrt(3))^4 is 49+20sqrt(6)

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expand (sqrt(2)+sqrt(3))^4

expand

(2 + 3)^{4}

49 + 206

Decimal Notation

97.98979 \dots

Solution steps

(2 + 3)^{4}

Apply binomial theorem:

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

a = 2, b = 3

= i = 0 \sum 4 (i 4) (2)^{(4 - i)} (3)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2)^{4} (3)^{0} : 4

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2)^{3} (3)^{1} : 86

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2)^{2} (3)^{2} : 36

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2)^{1} (3)^{3} : 126

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2)^{0} (3)^{4} : 9

= 4 + 86 + 36 + 126 + 9

4 + 86 + 36 + 126 + 9 = 49 + 206

= 49 + 206

(x - 2) ln (x)

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

(x + 2)^{3}

(y^{3} - y x^{2}) d x + x^{3} d y

(π - x)^{2}

What is expand (sqrt(2)+sqrt(3))^4 ?
The solution to expand (sqrt(2)+sqrt(3))^4 is 49+20sqrt(6)