What is expand (sqrt(2)+sqrt(3))^7 ?

The solution to expand (sqrt(2)+sqrt(3))^7 is 1079sqrt(2)+881sqrt(3)

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expand (sqrt(2)+sqrt(3))^7

expand

(2 + 3)^{7}

10792 + 8813

Decimal Notation

3051.87319 \dots

Solution steps

(2 + 3)^{7}

Apply binomial theorem:

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

a = 2, b = 3

= i = 0 \sum 7 (i 7) (2)^{(7 - i)} (3)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} (2)^{7} (3)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} (2)^{6} (3)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} (2)^{5} (3)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} (2)^{4} (3)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} (2)^{3} (3)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} (2)^{2} (3)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} (2)^{1} (3)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} (2)^{0} (3)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} (2)^{7} (3)^{0} : 82

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} (2)^{6} (3)^{1} : 563

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} (2)^{5} (3)^{2} : 2522

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} (2)^{4} (3)^{3} : 4203

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} (2)^{3} (3)^{4} : 6302

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} (2)^{2} (3)^{5} : 3783

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} (2)^{1} (3)^{6} : 1892

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} (2)^{0} (3)^{7} : 273

= 82 + 563 + 2522 + 4203 + 6302 + 3783 + 1892 + 273

82 + 563 + 2522 + 4203 + 6302 + 3783 + 1892 + 273 = 10792 + 8813

= 10792 + 8813

(2 + 3)^{5}

- csc^{2} (x) cot (x) (csc^{2} (x) - cot (x))

18 π (1 + \frac{π}{4})

(x^{2} - \frac{3 y}{4} + \frac{9}{7}) (\frac{x}{2} + \frac{3 y}{5} - 2)

h (4 x + h + 4 x)

What is expand (sqrt(2)+sqrt(3))^7 ?
The solution to expand (sqrt(2)+sqrt(3))^7 is 1079sqrt(2)+881sqrt(3)