en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x-1)^4

Solution

expand

(3 x - 1)^{4}

Solution

81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x + 1

Solution steps

(3 x - 1)^{4}

Apply binomial theorem:

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

a = 3 x, b = - 1

= i = 0 \sum 4 (i 4) (3 x)^{(4 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x)^{4} (- 1)^{0} : 81 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (- 1)^{1} : - 108 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (- 1)^{2} : 54 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} (- 1)^{3} : - 12 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (- 1)^{4} : 1

= 81 x^{4} - 108 x^{3} + 54 x^{2} - 12 x + 1

Popular Examples

expand (1-8xy)(8xy+1)expand

(1 - 8 x y) (8 x y + 1)

expand (3x-8)(3x+8)expand

(3 x - 8) (3 x + 8)

f (x) = x^{4} - 2

expand (x+2)(x+4)(x+6)expand

(x + 2) (x + 4) (x + 6)

simplify (-7x^3y^2)/(x^3y^2)simplify

\frac{- 7 x ^{3} y ^{2}}{x ^{3} y ^{2}}

Frequently Asked Questions (FAQ)

What is expand (3x-1)^4 ?
The solution to expand (3x-1)^4 is 81x^4-108x^3+54x^2-12x+1