Solve -(1-x^2)^2

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

Expand

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

Solution Steps

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

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

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

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

To find the opposite of 1-2x^{2}+x^{4}, find the opposite of each term.

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

Evaluate

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

Solution Steps

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

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

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

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

To find the opposite of 1-2x^{2}+x^{4}, find the opposite of each term.

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