$SA = 2\pi(6^2) + 2\pi(6)(2)$

Key concept: This is a simplification problem. The goal is to factor the expression correctly and keep track of the common terms.

Step by step

Start with

$$SA = 2\pi(6^2) + 2\pi(6)(2)$$

Step 1: Evaluate the powers and products

$$6^2=36$$

So

$$SA = 2\pi(36) + 2\pi(12)$$

Step 2: Factor out the common factor

Both terms have a factor of $2\pi(6)$:

$$SA = 2\pi(6)(6) + 2\pi(6)(2)$$

Factor out $2\pi(6)$:

$$SA = 2\pi(6)(6+2)$$

Step 3: Match the intended simplified form

Since $2\pi(6)=12\pi$,

$$SA = 12\pi(6+2)$$

This is also the same as

$$SA = 6\cdot 2\pi(6+2)$$

Pitfall alert

Do not combine $6^2$ with $2$ before evaluating the square. Also, be careful not to drop a factor when factoring the expression.

Try different conditions

If the expression were $SA=2\pi r^2+2\pi rh$, you would factor it as $2\pi r(r+h)$. The same factoring pattern applies here.

Further reading

surface area, factoring, common factor