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

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

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expand (3x-4)^4

expand

(3 x - 4)^{4}

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

Solution steps

(3 x - 4)^{4}

Apply binomial theorem:

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

a = 3 x, b = - 4

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

8 x + 16

(- x + 6)^{2}

(4 x - y)^{3}

\frac{32}{7}

(\frac{5}{4} x - \frac{1}{3})^{2}

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