What is expand (x-4)^5 ?

The solution to expand (x-4)^5 is x^5-20x^4+160x^3-640x^2+1280x-1024

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expand (x-4)^5

expand

(x - 4)^{5}

x^{5} - 20 x^{4} + 160 x^{3} - 640 x^{2} + 1280 x - 1024

Solution steps

(x - 4)^{5}

Apply binomial theorem:

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

a = x, b = - 4

= i = 0 \sum 5 (i 5) x^{(5 - i)} (- 4)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (- 4)^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (- 4)^{1} : - 20 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (- 4)^{2} : 160 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (- 4)^{3} : - 640 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (- 4)^{4} : 1280 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (- 4)^{5} : - 1024

= x^{5} - 20 x^{4} + 160 x^{3} - 640 x^{2} + 1280 x - 1024

(4 + i) (2 - i)

3 x^{3} + 9 x^{2} - 6 x

\frac{60}{6}

a (b + c)

(2 a + 1) (2 a - 1)

What is expand (x-4)^5 ?
The solution to expand (x-4)^5 is x^5-20x^4+160x^3-640x^2+1280x-1024