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

The solution to (x^2-1/2 x)^2 is x^4-x^3+(x^2)/4

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

simplify

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

x^{4} - x^{3} + \frac{x ^{2}}{4}

Solution steps

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

\frac{1}{2} x = \frac{x}{2}

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

Apply Perfect Square Formula:

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

a = x^{2}, b = \frac{x}{2}

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

Simplify

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

= x^{4} - x^{3} + \frac{x ^{2}}{4}

\frac{x}{2 x}

\frac{2}{x - 4} - 7 x

\frac{6 a ^{2} x ^{3}}{\frac{a ^{2} x}{5}}

(2 m)^{3}

- 11 x^{5} (- 9 x^{3} y^{4})