What is expand (x-1)^6 ?

The solution to expand (x-1)^6 is x^6-6x^5+15x^4-20x^3+15x^2-6x+1

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expand (x-1)^6

expand

(x - 1)^{6}

x^{6} - 6 x^{5} + 15 x^{4} - 20 x^{3} + 15 x^{2} - 6 x + 1

Solution steps

(x - 1)^{6}

Apply binomial theorem:

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

a = x, b = - 1

= i = 0 \sum 6 (i 6) x^{(6 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} (- 1)^{0} : x^{6}

Simplify

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

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- 1)^{2} : 15 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- 1)^{3} : - 20 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- 1)^{4} : 15 x^{2}

Simplify

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

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- 1)^{6} : 1

= x^{6} - 6 x^{5} + 15 x^{4} - 20 x^{3} + 15 x^{2} - 6 x + 1

\frac{\frac{4}{3 r - 1} - 4}{\frac{4}{3 r - 1} + 4}

(s - 3)^{3}

(x - \frac{7}{2})^{2}

\frac{60}{360}

- x^{2} - 4 x - 3

What is expand (x-1)^6 ?
The solution to expand (x-1)^6 is x^6-6x^5+15x^4-20x^3+15x^2-6x+1