Solve -(x^2+1)^2

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

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(x^{2}+1\right)^{2}.

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

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

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

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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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