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

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

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

expand

(3 + 2)^{4}

49 + 206

Decimal Notation

97.98979 \dots

Solution steps

(3 + 2)^{4}

Apply binomial theorem:

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

a = 3, b = 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= 9 + 126 + 36 + 86 + 4

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

= 49 + 206

y (x + y + 1) d x

lo g_{10} (2) (1 + x^{2})

\frac{x ^{2} - 4 x + 5}{x ( x + 1 ) \cdot ( x + 2 )}

(k + 2 i + j + 2) \times (k + ki + i + ij + j)^{2}

P (- 2, 1) Q (- 10, - 5)

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