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

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

Evaluate

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

Solution Steps

Multiply x^{2}+1 and x^{2}+1 to get \left(x^{2}+1\right)^{2}.

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

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

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

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

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

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

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

Expand

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

Solution Steps

Multiply x^{2}+1 and x^{2}+1 to get \left(x^{2}+1\right)^{2}.

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

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

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

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

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

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

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