What is expand (x^2-1/x)^2 ?

The solution to expand (x^2-1/x)^2 is (x^6-2x^3+1)/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x^2-1/x)^2

expand

(x^{2} - \frac{1}{x})^{2}

\frac{x ^{6} - 2 x ^{3} + 1}{x ^{2}}

Solution steps

(x^{2} - \frac{1}{x})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(x^{2} - \frac{1}{x})^{2} = (x^{2})^{2} - 2 x^{2} \frac{1}{x} + (\frac{1}{x})^{2}

= (x^{2})^{2} - 2 x^{2} \frac{1}{x} + (\frac{1}{x})^{2}

Simplify

(x^{2})^{2} - 2 x^{2} \frac{1}{x} + (\frac{1}{x})^{2} : \frac{x ^{6} - 2 x ^{3} + 1}{x ^{2}}

= \frac{x ^{6} - 2 x ^{3} + 1}{x ^{2}}

x (x + x + 1)

\frac{3 x - 1}{( x + 1 ) ^{2}}

- 7 (3 x - 5 y = 8)

What is expand (x^2-1/x)^2 ?
The solution to expand (x^2-1/x)^2 is (x^6-2x^3+1)/(x^2)