Solve the Quadratic Expression: (x+3)² + (x-3)²

To solve this problem, we'll follow these steps:

• Step 1: Expand $(x+3)^2$.
• Step 2: Expand $(x-3)^2$.
• Step 3: Simplify the expression by combining like terms.

Now, let's work through each step:
Step 1: Expand $(x+3)^2$ using the formula for the square of a sum:

$(x+3)^2 = x^2 + 2 \cdot x \cdot 3 + 3^2 = x^2 + 6x + 9$

Step 2: Expand $(x-3)^2$ using the formula for the square of a difference:

$(x-3)^2 = x^2 - 2 \cdot x \cdot 3 + 3^2 = x^2 - 6x + 9$

Step 3: Add the expanded expressions together and simplify:

$(x+3)^2 + (x-3)^2 = (x^2 + 6x + 9) + (x^2 - 6x + 9)$

$(x^2 + 6x + 9) + (x^2 - 6x + 9) = 2x^2 + 0x + 18 = 2x^2 + 18$

Therefore, the solution to the problem is $2x^2 + 18$.