What is expand (3x-y)^4 ?

The solution to expand (3x-y)^4 is 81x^4-108x^3y+54x^2y^2-12xy^3+y^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x-y)^4

expand

(3 x - y)^{4}

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

Solution steps

(3 x - y)^{4}

Apply binomial theorem:

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

a = 3 x, b = - y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{24}{7} - \frac{21}{2} + \frac{11}{14}

8 - \frac{2}{3}

\frac{2 x}{7} + \frac{9}{2}

(22)^{4}

\frac{1 - \frac{12}{13}}{2}

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