Solve (n^2+2)^2-4n^2+1

$$( n ^ { 2 } + 2 ) ^ { 2 } - 4 n ^ { 2 } + 1$$

Evaluate

$$n^{4}+5$$

Solution Steps

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

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

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

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

Combine 4n^{2} and -4n^{2} to get 0.

$$n^{4}+4+1$$

Add 4 and 1 to get 5.

$$n^{4}+5$$

Expand

$$n^{4}+5$$

Solution Steps

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

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

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

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

Combine 4n^{2} and -4n^{2} to get 0.

$$n^{4}+4+1$$

Add 4 and 1 to get 5.

$$n^{4}+5$$