Solve 4(3-1/2x^2)^2-3

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

Evaluate

$$\left(6-x^{2}\right)^{2}-3$$

Solution Steps

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

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

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

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

Use the distributive property to multiply 4 by 9-3x^{2}+\frac{1}{4}x^{4}.

$$36-12x^{2}+x^{4}-3$$

Subtract 3 from 36 to get 33.

$$33-12x^{2}+x^{4}$$

Expand

$$x^{4}-12x^{2}+33$$

Solution Steps

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

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

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

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

Use the distributive property to multiply 4 by 9-3x^{2}+\frac{1}{4}x^{4}.

$$36-12x^{2}+x^{4}-3$$

Subtract 3 from 36 to get 33.

$$33-12x^{2}+x^{4}$$