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

0.01020 \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

- \frac{( x + 12 ) ( x + 8 ) ( x - 0 ) ( x - 12 )}{10240}

(1 + t) y^{''} (t) + (- 1 + t) y^{'} (t) - 2 y

(f \circ g) (2 x + 1) - 3

d x d (x^{6} + 3 x^{4} + 7 x^{2})

\frac{s}{( s ^{2} + n ^{2} ) ( s - 4 )}

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