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

The solution to expand (4x^3-3sqrt(x))^4 is 256x^{12}-768sqrt(x^{19)}+864x^7-432sqrt(x^9)+81x^2

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expand (4x^3-3sqrt(x))^4

expand

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

256 x^{12} - 768 x^{19} + 864 x^{7} - 432 x^{9} + 81 x^{2}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (4 x^{3})^{4} (- 3 x)^{0} : 256 x^{12}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (4 x^{3})^{3} (- 3 x)^{1} : - 768 x^{9} x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (4 x^{3})^{2} (- 3 x)^{2} : 864 x^{7}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (4 x^{3})^{0} (- 3 x)^{4} : 81 x^{2}

= 256 x^{12} - 768 x^{9} x + 864 x^{7} - 432 x^{3} (x)^{3} + 81 x^{2}

Simplify

256 x^{12} - 768 x^{9} x + 864 x^{7} - 432 x^{3} (x)^{3} + 81 x^{2} : 256 x^{12} - 768 x^{\frac{19}{2}} + 864 x^{7} - 432 x^{\frac{9}{2}} + 81 x^{2}

= 256 x^{12} - 768 x^{\frac{19}{2}} + 864 x^{7} - 432 x^{\frac{9}{2}} + 81 x^{2}

Simplify

256 x^{12} - 768 x^{\frac{19}{2}} + 864 x^{7} - 432 x^{\frac{9}{2}} + 81 x^{2} : 256 x^{12} - 768 x^{19} + 864 x^{7} - 432 x^{9} + 81 x^{2}

= 256 x^{12} - 768 x^{19} + 864 x^{7} - 432 x^{9} + 81 x^{2}

\frac{5}{2} cos (\frac{1}{2}) (x + \frac{π}{2})

- 42 (- 14 e^{- 7 x^{2}} x^{2} + e^{- 7 x^{2}})

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

(e^{x} + 2 x)^{2}

2^{x} (2^{x} \cdot 2)

What is expand (4x^3-3sqrt(x))^4 ?
The solution to expand (4x^3-3sqrt(x))^4 is 256x^{12}-768sqrt(x^{19)}+864x^7-432sqrt(x^9)+81x^2