What is expand (x-1)^8 ?

The solution to expand (x-1)^8 is x^8-8x^7+28x^6-56x^5+70x^4-56x^3+28x^2-8x+1

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expand (x-1)^8

expand

(x - 1)^{8}

x^{8} - 8 x^{7} + 28 x^{6} - 56 x^{5} + 70 x^{4} - 56 x^{3} + 28 x^{2} - 8 x + 1

Solution steps

(x - 1)^{8}

Apply binomial theorem:

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

a = x, b = - 1

= i = 0 \sum 8 (i 8) x^{(8 - i)} (- 1)^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} (- 1)^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} (- 1)^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} (- 1)^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} (- 1)^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} (- 1)^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} (- 1)^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} (- 1)^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} (- 1)^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} (- 1)^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} (- 1)^{0} : x^{8}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} (- 1)^{1} : - 8 x^{7}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} (- 1)^{2} : 28 x^{6}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} (- 1)^{3} : - 56 x^{5}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} (- 1)^{4} : 70 x^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} (- 1)^{5} : - 56 x^{3}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} (- 1)^{6} : 28 x^{2}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} (- 1)^{7} : - 8 x

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} (- 1)^{8} : 1

= x^{8} - 8 x^{7} + 28 x^{6} - 56 x^{5} + 70 x^{4} - 56 x^{3} + 28 x^{2} - 8 x + 1

12 (x - y)^{2} + 7 (x - y) - 12

\frac{1}{2 x} + \frac{1}{2 x}

\frac{1}{3} \cdot \frac{3}{1}

(30 x - 1)^{2}

x + \frac{x}{3}

What is expand (x-1)^8 ?
The solution to expand (x-1)^8 is x^8-8x^7+28x^6-56x^5+70x^4-56x^3+28x^2-8x+1