What is expand (x-sqrt(7))^6 ?

The solution to expand (x-sqrt(7))^6 is x^6-6sqrt(7)x^5+105x^4-140sqrt(7)x^3+735x^2-294sqrt(7)x+343

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expand (x-sqrt(7))^6

expand

(x - 7)^{6}

x^{6} - 67 x^{5} + 105 x^{4} - 1407 x^{3} + 735 x^{2} - 2947 x + 343

Solution steps

(x - 7)^{6}

Apply binomial theorem:

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

a = x, b = - 7

= i = 0 \sum 6 (i 6) x^{(6 - i)} (- 7)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} (- 7)^{0} : x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} (- 7)^{1} : - 67 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- 7)^{2} : 105 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- 7)^{3} : - 1407 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- 7)^{4} : 735 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} (- 7)^{5} : - 2947 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- 7)^{6} : 343

= x^{6} - 67 x^{5} + 105 x^{4} - 1407 x^{3} + 735 x^{2} - 2947 x + 343

- \frac{1}{12} (x - 3) (x - 11)

(5 - x - 2)^{2}

B (3, 6, - 9) A (- 4, 8, - 5)

\frac{1 0 ^{6} K}{( i w + 1 0 ^{2} ) ^{3}}

\frac{( p - 11 ) r ( p - 6 )}{2 ( p ^{2} - 12 p + 36 - 5 r )}

What is expand (x-sqrt(7))^6 ?
The solution to expand (x-sqrt(7))^6 is x^6-6sqrt(7)x^5+105x^4-140sqrt(7)x^3+735x^2-294sqrt(7)x+343