What is expand (x-3)^7 ?

The solution to expand (x-3)^7 is x^7-21x^6+189x^5-945x^4+2835x^3-5103x^2+5103x-2187

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expand (x-3)^7

expand

(x - 3)^{7}

x^{7} - 21 x^{6} + 189 x^{5} - 945 x^{4} + 2835 x^{3} - 5103 x^{2} + 5103 x - 2187

Solution steps

(x - 3)^{7}

Apply binomial theorem:

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

a = x, b = - 3

= i = 0 \sum 7 (i 7) x^{(7 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} (- 3)^{0} : x^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} x^{6} (- 3)^{1} : - 21 x^{6}

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} (- 3)^{2} : 189 x^{5}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} (- 3)^{3} : - 945 x^{4}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} (- 3)^{4} : 2835 x^{3}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} (- 3)^{5} : - 5103 x^{2}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} x^{1} (- 3)^{6} : 5103 x

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} (- 3)^{7} : - 2187

= x^{7} - 21 x^{6} + 189 x^{5} - 945 x^{4} + 2835 x^{3} - 5103 x^{2} + 5103 x - 2187

\frac{18 - i}{- 3 - 4 i}

2 x (3 x - 4)

(9 x^{2} - 4 y^{2}) (x^{2} - 25 y^{2})

x^{4} + 4 x^{2} + 16

2 1^{3}

What is expand (x-3)^7 ?
The solution to expand (x-3)^7 is x^7-21x^6+189x^5-945x^4+2835x^3-5103x^2+5103x-2187