Solve (a+a^-1)^2

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

Evaluate

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

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+a^{-1}\right)^{2}.

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

Multiply a and a^{-1} to get 1.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$a^{2}+2+a^{-2}$$

Expand

$$a^{2}+2+\frac{1}{a^{2}}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+a^{-1}\right)^{2}.

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

Multiply a and a^{-1} to get 1.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$a^{2}+2+a^{-2}$$