What is expand (x-1)^7 ?

The solution to expand (x-1)^7 is x^7-7x^6+21x^5-35x^4+35x^3-21x^2+7x-1

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expand (x-1)^7

expand

(x - 1)^{7}

x^{7} - 7 x^{6} + 21 x^{5} - 35 x^{4} + 35 x^{3} - 21 x^{2} + 7 x - 1

Solution steps

(x - 1)^{7}

Apply binomial theorem:

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

a = x, b = - 1

= i = 0 \sum 7 (i 7) x^{(7 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} (- 1)^{0} : x^{7}

Simplify

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

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} (- 1)^{2} : 21 x^{5}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} (- 1)^{3} : - 35 x^{4}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} (- 1)^{4} : 35 x^{3}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} (- 1)^{5} : - 21 x^{2}

Simplify

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

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} (- 1)^{7} : - 1

= x^{7} - 7 x^{6} + 21 x^{5} - 35 x^{4} + 35 x^{3} - 21 x^{2} + 7 x - 1

(- 2 - 2 i) (- 4 + 6 i)

\frac{2 5 - 3}{5 - 2} + \frac{3 5 - 2}{2 - 5}

lo g_{5} (2^{- l o g_{2} (5)})

3 x 8 x^{3} + 5 x 18 x^{3}

(6 x^{2} - x + 3) - (- 5 x^{2} + 10 x - 1)

What is expand (x-1)^7 ?
The solution to expand (x-1)^7 is x^7-7x^6+21x^5-35x^4+35x^3-21x^2+7x-1