What is expand (-6x^3+2)^4 ?

The solution to expand (-6x^3+2)^4 is 1296x^{12}-1728x^9+864x^6-192x^3+16

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expand (-6x^3+2)^4

expand

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

1296 x^{12} - 1728 x^{9} + 864 x^{6} - 192 x^{3} + 16

Solution steps

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

Apply binomial theorem:

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

a = - 6 x^{3}, b = 2

= i = 0 \sum 4 (i 4) (- 6 x^{3})^{(4 - i)} \cdot 2^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (- 6 x^{3})^{4} \cdot 2^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (- 6 x^{3})^{3} \cdot 2^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (- 6 x^{3})^{2} \cdot 2^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (- 6 x^{3})^{1} \cdot 2^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (- 6 x^{3})^{0} \cdot 2^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (- 6 x^{3})^{4} \cdot 2^{0} : 1296 x^{12}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (- 6 x^{3})^{3} \cdot 2^{1} : - 1728 x^{9}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (- 6 x^{3})^{2} \cdot 2^{2} : 864 x^{6}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (- 6 x^{3})^{1} \cdot 2^{3} : - 192 x^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (- 6 x^{3})^{0} \cdot 2^{4} : 16

= 1296 x^{12} - 1728 x^{9} + 864 x^{6} - 192 x^{3} + 16

\frac{( 2 x - 4 )}{( x ^{2} - 4 )}

(5 z^{- 3} \cdot y^{3} \cdot z^{- 7})^{- 1}

56 x + 337 x + 6

(x - t)^{3}

\frac{( 27 s ^{3} - 64 )}{( 3 s - 4 )}

What is expand (-6x^3+2)^4 ?
The solution to expand (-6x^3+2)^4 is 1296x^{12}-1728x^9+864x^6-192x^3+16