What is expand (x-4)^6 ?

The solution to expand (x-4)^6 is x^6-24x^5+240x^4-1280x^3+3840x^2-6144x+4096

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x-4)^6

expand

(x - 4)^{6}

x^{6} - 24 x^{5} + 240 x^{4} - 1280 x^{3} + 3840 x^{2} - 6144 x + 4096

Solution steps

(x - 4)^{6}

Apply binomial theorem:

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

a = x, b = - 4

= i = 0 \sum 6 (i 6) x^{(6 - i)} (- 4)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} (- 4)^{0} : x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} (- 4)^{1} : - 24 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- 4)^{2} : 240 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- 4)^{3} : - 1280 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- 4)^{4} : 3840 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} (- 4)^{5} : - 6144 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- 4)^{6} : 4096

= x^{6} - 24 x^{5} + 240 x^{4} - 1280 x^{3} + 3840 x^{2} - 6144 x + 4096

(x - 3) (x - 1) (x + 2)

(x - 8) (x - 9)

4 x^{2} + 15 x + 14

(x - 2) (x - 4) (x - 5)

\frac{18}{27 x + 27}

What is expand (x-4)^6 ?
The solution to expand (x-4)^6 is x^6-24x^5+240x^4-1280x^3+3840x^2-6144x+4096