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

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

Evaluate

$$\frac{\left(6x^{2}-1\right)^{2}}{4}$$

Solution Steps

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

$$9\left(x^{2}\right)^{2}-3x^{2}+\frac{1}{4}$$

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

$$9x^{4}-3x^{2}+\frac{1}{4}$$

Expand

$$9x^{4}-3x^{2}+\frac{1}{4}$$

Solution Steps

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

$$9\left(x^{2}\right)^{2}-3x^{2}+\frac{1}{4}$$

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

$$9x^{4}-3x^{2}+\frac{1}{4}$$