What is expand (-sqrt(3)+j)^6 ?

The solution to expand (-sqrt(3)+j)^6 is 27-54sqrt(3)j+135j^2-60sqrt(3)j^3+45j^4-6sqrt(3)j^5+j^6

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expand (-sqrt(3)+j)^6

expand

(- 3 + j)^{6}

27 - 543 j + 135 j^{2} - 603 j^{3} + 45 j^{4} - 63 j^{5} + j^{6}

Solution steps

(- 3 + j)^{6}

Apply binomial theorem:

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

a = - 3, b = j

= i = 0 \sum 6 (i 6) (- 3)^{(6 - i)} j^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (- 3)^{6} j^{0} : 27

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (- 3)^{5} j^{1} : - 543 j

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (- 3)^{4} j^{2} : 135 j^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (- 3)^{3} j^{3} : - 603 j^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (- 3)^{2} j^{4} : 45 j^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (- 3)^{1} j^{5} : - 63 j^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (- 3)^{0} j^{6} : j^{6}

= 27 - 543 j + 135 j^{2} - 603 j^{3} + 45 j^{4} - 63 j^{5} + j^{6}

\frac{9 + h - 3}{h}

23 (x - \frac{π}{6})

so l v e^{7} - 3 (s + 1)

A (- 4, 6) B (3, - 8)

\frac{d}{d y} ((x) (c (y + 1)^{2}))

What is expand (-sqrt(3)+j)^6 ?
The solution to expand (-sqrt(3)+j)^6 is 27-54sqrt(3)j+135j^2-60sqrt(3)j^3+45j^4-6sqrt(3)j^5+j^6