What is expand (4x^2-3/x)^5 ?

The solution to expand (4x^2-3/x)^5 is 1024x^{10}-3840x^7+5760x^4-4320x+(1620)/(x^2)-(243)/(x^5)

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expand (4x^2-3/x)^5

expand

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

1024 x^{10} - 3840 x^{7} + 5760 x^{4} - 4320 x + \frac{1620}{x ^{2}} - \frac{243}{x ^{5}}

Solution steps

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

Apply binomial theorem:

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

a = 4 x^{2}, b = - \frac{3}{x}

= i = 0 \sum 5 (i 5) (4 x^{2})^{(5 - i)} (- \frac{3}{x})^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (4 x^{2})^{5} (- \frac{3}{x})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (4 x^{2})^{4} (- \frac{3}{x})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (4 x^{2})^{3} (- \frac{3}{x})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (4 x^{2})^{2} (- \frac{3}{x})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (4 x^{2})^{1} (- \frac{3}{x})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (4 x^{2})^{0} (- \frac{3}{x})^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (4 x^{2})^{5} (- \frac{3}{x})^{0} : 1024 x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 x^{2})^{4} (- \frac{3}{x})^{1} : - 3840 x^{7}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (4 x^{2})^{3} (- \frac{3}{x})^{2} : 5760 x^{4}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (4 x^{2})^{2} (- \frac{3}{x})^{3} : - 4320 x

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (4 x^{2})^{1} (- \frac{3}{x})^{4} : \frac{1620}{x ^{2}}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (4 x^{2})^{0} (- \frac{3}{x})^{5} : - \frac{243}{x ^{5}}

= 1024 x^{10} - 3840 x^{7} + 5760 x^{4} - 4320 x + \frac{1620}{x ^{2}} - \frac{243}{x ^{5}}

\frac{( ( k + 1 ) ^{2} ( ( k + 1 ) + 1 ) ^{2} )}{4}

(x^{3} - x + 30)^{7}

(12 n + 6) -!! (10 n - 2)

(8, - 3) y (2, 1)

\frac{a ^{2} ( 12 a ^{2} - 5 ) ^{2}}{4}

What is expand (4x^2-3/x)^5 ?
The solution to expand (4x^2-3/x)^5 is 1024x^{10}-3840x^7+5760x^4-4320x+(1620)/(x^2)-(243)/(x^5)