en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (a-sqrt(b))^{12}

Solution

expand

(a - b)^{12}

Solution

a^{12} - 12 a^{11} b + 66 a^{10} b - 220 a^{9} b b + 495 a^{8} b^{2} - 792 a^{7} b^{2} b + 924 a^{6} b^{3} - 792 a^{5} b^{3} b + 495 a^{4} b^{4} - 220 a^{3} b^{4} b + 66 a^{2} b^{5} - 12 a b^{5} b + b^{6}

Solution steps

(a - b)^{12}

Apply binomial theorem:

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

a = a, b = - b

= i = 0 \sum 12 (i 12) a^{(12 - i)} (- b)^{i}

Expand summation

= \frac{12 !}{0 ! ( 12 - 0 ) !} a^{12} (- b)^{0} + \frac{12 !}{1 ! ( 12 - 1 ) !} a^{11} (- b)^{1} + \frac{12 !}{2 ! ( 12 - 2 ) !} a^{10} (- b)^{2} + \frac{12 !}{3 ! ( 12 - 3 ) !} a^{9} (- b)^{3} + \frac{12 !}{4 ! ( 12 - 4 ) !} a^{8} (- b)^{4} + \frac{12 !}{5 ! ( 12 - 5 ) !} a^{7} (- b)^{5} + \frac{12 !}{6 ! ( 12 - 6 ) !} a^{6} (- b)^{6} + \frac{12 !}{7 ! ( 12 - 7 ) !} a^{5} (- b)^{7} + \frac{12 !}{8 ! ( 12 - 8 ) !} a^{4} (- b)^{8} + \frac{12 !}{9 ! ( 12 - 9 ) !} a^{3} (- b)^{9} + \frac{12 !}{10 ! ( 12 - 10 ) !} a^{2} (- b)^{10} + \frac{12 !}{11 ! ( 12 - 11 ) !} a^{1} (- b)^{11} + \frac{12 !}{12 ! ( 12 - 12 ) !} a^{0} (- b)^{12}

Simplify

\frac{12 !}{0 ! ( 12 - 0 ) !} a^{12} (- b)^{0} : a^{12}

Simplify

\frac{12 !}{1 ! ( 12 - 1 ) !} a^{11} (- b)^{1} : - 12 a^{11} b

Simplify

\frac{12 !}{2 ! ( 12 - 2 ) !} a^{10} (- b)^{2} : 66 a^{10} b

Simplify

\frac{12 !}{3 ! ( 12 - 3 ) !} a^{9} (- b)^{3} : - 220 a^{9} (b)^{3}

Simplify

\frac{12 !}{4 ! ( 12 - 4 ) !} a^{8} (- b)^{4} : 495 a^{8} b^{2}

Simplify

\frac{12 !}{5 ! ( 12 - 5 ) !} a^{7} (- b)^{5} : - 792 a^{7} (b)^{5}

Simplify

\frac{12 !}{6 ! ( 12 - 6 ) !} a^{6} (- b)^{6} : 924 a^{6} b^{3}

Simplify

\frac{12 !}{7 ! ( 12 - 7 ) !} a^{5} (- b)^{7} : - 792 a^{5} (b)^{7}

Simplify

\frac{12 !}{8 ! ( 12 - 8 ) !} a^{4} (- b)^{8} : 495 a^{4} b^{4}

Simplify

\frac{12 !}{9 ! ( 12 - 9 ) !} a^{3} (- b)^{9} : - 220 a^{3} (b)^{9}

Simplify

\frac{12 !}{10 ! ( 12 - 10 ) !} a^{2} (- b)^{10} : 66 a^{2} b^{5}

Simplify

\frac{12 !}{11 ! ( 12 - 11 ) !} a^{1} (- b)^{11} : - 12 a (b)^{11}

Simplify

\frac{12 !}{12 ! ( 12 - 12 ) !} a^{0} (- b)^{12} : b^{6}

= a^{12} - 12 a^{11} b + 66 a^{10} b - 220 a^{9} (b)^{3} + 495 a^{8} b^{2} - 792 a^{7} (b)^{5} + 924 a^{6} b^{3} - 792 a^{5} (b)^{7} + 495 a^{4} b^{4} - 220 a^{3} (b)^{9} + 66 a^{2} b^{5} - 12 a (b)^{11} + b^{6}

(b)^{3} = b b

(b)^{5} = b^{2} b

(b)^{7} = b^{3} b

(b)^{9} = b^{4} b

(b)^{11} = b^{5} b

= a^{12} - 12 a^{11} b + 66 a^{10} b - 220 a^{9} b b + 495 a^{8} b^{2} - 792 a^{7} b^{2} b + 924 a^{6} b^{3} - 792 a^{5} b^{3} b + 495 a^{4} b^{4} - 220 a^{3} b^{4} b + 66 a^{2} b^{5} - 12 a b^{5} b + b^{6}

Popular Examples

expand (-x+11)/(3x(4x-3))expand

\frac{- x + 11}{3 x ( 4 x - 3 )}

expand (pi/4+1/2)(x-1)expand

(\frac{π}{4} + \frac{1}{2}) (x - 1)

simplify (1+2sqrt(y))^2 simplify

(1 + 2 y)^{2}

simplify (sin(x)-1)(cos(x)-1/2)simplify

(sin (x) - 1) (cos (x) - \frac{1}{2})

derivative of (2(x-3+2/(x+1)))

\frac{d}{d x} ((2) (x - 3 + \frac{2}{x + 1}))

Frequently Asked Questions (FAQ)

What is expand (a-sqrt(b))^{12} ?
The solution to expand (a-sqrt(b))^{12} is