Solve (x^2-2)^2-(x^2-2)-2

$$( x ^ { 2 } - 2 ) ^ { 2 } - ( x ^ { 2 } - 2 ) - 2$$

Evaluate

$$x^{4}-5x^{2}+4$$

Solution Steps

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

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

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

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

To find the opposite of x^{2}-2, find the opposite of each term.

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

Combine -4x^{2} and -x^{2} to get -5x^{2}.

$$x^{4}-5x^{2}+4+2-2$$

Add 4 and 2 to get 6.

$$x^{4}-5x^{2}+6-2$$

Subtract 2 from 6 to get 4.

$$x^{4}-5x^{2}+4$$

Expand

$$x^{4}-5x^{2}+4$$

Solution Steps

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

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

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

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

To find the opposite of x^{2}-2, find the opposite of each term.

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

Combine -4x^{2} and -x^{2} to get -5x^{2}.

$$x^{4}-5x^{2}+4+2-2$$

Add 4 and 2 to get 6.

$$x^{4}-5x^{2}+6-2$$

Subtract 2 from 6 to get 4.

$$x^{4}-5x^{2}+4$$