Solve (x^3-1/2)^2

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

Evaluate

$$\frac{\left(2x^{3}-1\right)^{2}}{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{3}-\frac{1}{2}\right)^{2}.

$$\left(x^{3}\right)^{2}-x^{3}+\frac{1}{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}-x^{3}+\frac{1}{4}$$

Expand

$$x^{6}-x^{3}+\frac{1}{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{3}-\frac{1}{2}\right)^{2}.

$$\left(x^{3}\right)^{2}-x^{3}+\frac{1}{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}-x^{3}+\frac{1}{4}$$