Solve left(-(x^2+1right)^2

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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