What is expand (x-4)^7 ?

The solution to expand (x-4)^7 is x^7-28x^6+336x^5-2240x^4+8960x^3-21504x^2+28672x-16384

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expand (x-4)^7

expand

(x - 4)^{7}

x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} - 21504 x^{2} + 28672 x - 16384

Solution steps

(x - 4)^{7}

Apply binomial theorem:

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

a = x, b = - 4

= i = 0 \sum 7 (i 7) x^{(7 - i)} (- 4)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} (- 4)^{0} : x^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} x^{6} (- 4)^{1} : - 28 x^{6}

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} (- 4)^{2} : 336 x^{5}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} (- 4)^{3} : - 2240 x^{4}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} (- 4)^{4} : 8960 x^{3}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} (- 4)^{5} : - 21504 x^{2}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} x^{1} (- 4)^{6} : 28672 x

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} (- 4)^{7} : - 16384

= x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} - 21504 x^{2} + 28672 x - 16384

(x - 4)^{6}

\frac{11}{16} + \frac{11}{20}

\frac{1}{2} \div 1 \frac{1}{2}

55 \times 5

\frac{15}{30}

What is expand (x-4)^7 ?
The solution to expand (x-4)^7 is x^7-28x^6+336x^5-2240x^4+8960x^3-21504x^2+28672x-16384