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

The solution to expand (3x-4y)^4 is 81x^4-432x^3y+864x^2y^2-768xy^3+256y^4

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expand (3x-4y)^4

expand

(3 x - 4 y)^{4}

81 x^{4} - 432 x^{3} y + 864 x^{2} y^{2} - 768 x y^{3} + 256 y^{4}

Solution steps

(3 x - 4 y)^{4}

Apply binomial theorem:

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

a = 3 x, b = - 4 y

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (- 4 y)^{1} : - 432 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (- 4 y)^{2} : 864 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} (- 4 y)^{3} : - 768 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (- 4 y)^{4} : 256 y^{4}

= 81 x^{4} - 432 x^{3} y + 864 x^{2} y^{2} - 768 x y^{3} + 256 y^{4}

\frac{9 x}{8} + \frac{7}{3}

- x^{2} - 4 x - 1

20 \times \frac{1}{4}

12 x + x

\frac{44}{11}

What is expand (3x-4y)^4 ?
The solution to expand (3x-4y)^4 is 81x^4-432x^3y+864x^2y^2-768xy^3+256y^4