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

The solution to expand (3x^4-3)^4 is 81x^{16}-324x^{12}+486x^8-324x^4+81

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expand (3x^4-3)^4

expand

(3 x^{4} - 3)^{4}

81 x^{16} - 324 x^{12} + 486 x^{8} - 324 x^{4} + 81

Solution steps

(3 x^{4} - 3)^{4}

Apply binomial theorem:

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

a = 3 x^{4}, b = - 3

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x^{4})^{4} (- 3)^{0} : 81 x^{16}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x^{4})^{3} (- 3)^{1} : - 324 x^{12}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x^{4})^{2} (- 3)^{2} : 486 x^{8}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x^{4})^{1} (- 3)^{3} : - 324 x^{4}

Simplify

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

= 81 x^{16} - 324 x^{12} + 486 x^{8} - 324 x^{4} + 81

24 x^{3} + x^{2} - 1

(\frac{1}{m ^{2}})^{0}

(\frac{3 y}{2 - 2 z})^{3}

5 (\frac{1 + 1}{n})^{n}

r^{9} + r^{4} + r^{2}

What is expand (3x^4-3)^4 ?
The solution to expand (3x^4-3)^4 is 81x^{16}-324x^{12}+486x^8-324x^4+81