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

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

Evaluate

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

Solution Steps

Multiply x^{2}-\frac{1}{2} and x^{2}-\frac{1}{2} to get \left(x^{2}-\frac{1}{2}\right)^{2}.

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

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

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

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

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

Expand

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

Solution Steps

Multiply x^{2}-\frac{1}{2} and x^{2}-\frac{1}{2} to get \left(x^{2}-\frac{1}{2}\right)^{2}.

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

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

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

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

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