Solve (1f^2+1)^2=

$$( 1 f ^ { 2 } + 1 ) ^ { 2 } =$$

Evaluate

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

Solution Steps

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

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

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

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

Expand

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

Solution Steps

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

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

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

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