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}

15 x^{2} y^{2} z + 20 x^{3} y^{3} z^{2}

3 a^{x + 5} + 19 a^{x + 3} - 10 a^{x + 4} - 8 a^{x + 2} + 5 a^{x + 1}

- 4 x^{2} + 100 x - 60

\frac{1}{3 n ( 4 n \cdot 2 - 1 )}

3 x^{2} - 4 x + 3 - (7 x^{2} + 4 x - 4)

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