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

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

Evaluate

$$\frac{\left(x\left(2x-1\right)\right)^{2}}{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-\frac{1}{2}x\right)^{2}.

$$\left(x^{2}\right)^{2}-x^{2}x+\frac{1}{4}x^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-x^{2}x+\frac{1}{4}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-x^{3}+\frac{1}{4}x^{2}$$

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-\frac{1}{2}x\right)^{2}.

$$\left(x^{2}\right)^{2}-x^{2}x+\frac{1}{4}x^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-x^{2}x+\frac{1}{4}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-x^{3}+\frac{1}{4}x^{2}$$