What is expand (a^2-1/a)^4 ?

The solution to expand (a^2-1/a)^4 is a^8-4a^5+6a^2-4/a+1/(a^4)

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expand (a^2-1/a)^4

expand

(a^{2} - \frac{1}{a})^{4}

a^{8} - 4 a^{5} + 6 a^{2} - \frac{4}{a} + \frac{1}{a ^{4}}

Solution steps

(a^{2} - \frac{1}{a})^{4}

Apply binomial theorem:

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

a = a^{2}, b = - \frac{1}{a}

= i = 0 \sum 4 (i 4) (a^{2})^{(4 - i)} (- \frac{1}{a})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (a^{2})^{4} (- \frac{1}{a})^{0} : a^{8}

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (a^{2})^{2} (- \frac{1}{a})^{2} : 6 a^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (a^{2})^{1} (- \frac{1}{a})^{3} : - \frac{4}{a}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (a^{2})^{0} (- \frac{1}{a})^{4} : \frac{1}{a ^{4}}

= a^{8} - 4 a^{5} + 6 a^{2} - \frac{4}{a} + \frac{1}{a ^{4}}

(7) (2 + 23)

(x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

2 (2 + 3)

(z - 2 i)^{2}

\frac{2 ( x + h ) + 1 - 2 x + 1}{h}

What is expand (a^2-1/a)^4 ?
The solution to expand (a^2-1/a)^4 is a^8-4a^5+6a^2-4/a+1/(a^4)