Solve (4n^2+1)^2

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

Expand

$$16n^{4}+8n^{2}+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4n^{2}+1\right)^{2}.

$$16\left(n^{2}\right)^{2}+8n^{2}+1$$

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

$$16n^{4}+8n^{2}+1$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4n^{2}+1\right)^{2}.

$$16\left(n^{2}\right)^{2}+8n^{2}+1$$

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

$$16n^{4}+8n^{2}+1$$