What is expand (x-sqrt(2))^6 ?

The solution to expand (x-sqrt(2))^6 is x^6-6sqrt(2)x^5+30x^4-40sqrt(2)x^3+60x^2-24sqrt(2)x+8

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expand (x-sqrt(2))^6

expand

(x - 2)^{6}

x^{6} - 62 x^{5} + 30 x^{4} - 402 x^{3} + 60 x^{2} - 242 x + 8

Solution steps

(x - 2)^{6}

Apply binomial theorem:

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

a = x, b = - 2

= i = 0 \sum 6 (i 6) x^{(6 - i)} (- 2)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} (- 2)^{0} : x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} (- 2)^{1} : - 62 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- 2)^{2} : 30 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- 2)^{3} : - 402 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- 2)^{4} : 60 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} (- 2)^{5} : - 242 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- 2)^{6} : 8

= x^{6} - 62 x^{5} + 30 x^{4} - 402 x^{3} + 60 x^{2} - 242 x + 8

3 (5 x + 3 y = 93)

(4 + x)^{2}

\frac{3 ( 4 π + 3 3 )}{400 π}

(a + b) (a + b)

\frac{10 x ^{2} ( 20 x - 333 )}{( 10 x - 111 ) ^{2}}

What is expand (x-sqrt(2))^6 ?
The solution to expand (x-sqrt(2))^6 is x^6-6sqrt(2)x^5+30x^4-40sqrt(2)x^3+60x^2-24sqrt(2)x+8