What is expand (-1-sqrt(3))^4 ?

The solution to expand (-1-sqrt(3))^4 is 28+16sqrt(3)

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expand (-1-sqrt(3))^4

expand

(- 1 - 3)^{4}

28 + 163

Decimal Notation

55.71281 \dots

Solution steps

(- 1 - 3)^{4}

Apply binomial theorem:

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

a = - 1, b = - 3

= i = 0 \sum 4 (i 4) (- 1)^{(4 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (- 1)^{4} (- 3)^{0} : 1

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (- 1)^{3} (- 3)^{1} : 43

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (- 1)^{2} (- 3)^{2} : 18

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (- 1)^{1} (- 3)^{3} : 123

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (- 1)^{0} (- 3)^{4} : 9

= 1 + 43 + 18 + 123 + 9

1 + 43 + 18 + 123 + 9 = 28 + 163

= 28 + 163

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What is expand (-1-sqrt(3))^4 ?
The solution to expand (-1-sqrt(3))^4 is 28+16sqrt(3)