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

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

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expand (x-3y)^4

expand

(x - 3 y)^{4}

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

Solution steps

(x - 3 y)^{4}

Apply binomial theorem:

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

a = x, b = - 3 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(n^{2} - 2 n + 1) (n^{2} - 1)

\frac{8 x y}{2 x ^{3} y ^{7}}

125 \frac{1}{3}

1 - e^{- \frac{3}{4}}

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