Solve the Expression: 2² + 12 + 3² Step by Step

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

• Step 1: Calculate each square.
• Step 2: Add these results.
• Step 3: Attempt to express it in a specific form, looking for a pattern based on known formulas.

Now, let's work through each step:

Step 1: Calculate the squared terms separately:
$2^2 = 4$
$3^2 = 9$

Step 2: Add these results along with the constant 12:
$4 + 12 + 9 = 25$

Step 3: Express 25 as a square of a sum.
Notice that $25 = (5)^2$.
We must check if this can be represented in the form $(a + b)^2 = a^2 + 2ab + b^2$.

The expression $(2+3)^2$ expands as follows:
$(2+3)^2 = 2^2 + 2 \cdot 2 \cdot 3 + 3^2 = 4 + 12 + 9$

The left-hand side $(2+3)^2$ perfectly matches our computed right-hand side $4 + 12 + 9$, verifying that this is correct.

Therefore, the expression can indeed be simplified as: $(2+3)^2$.