Solve: 49 - 2 × 21 + 9 Using Order of Operations

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

• Step 1: Simplify the given expression using order of operations.
• Step 2: Match the simplified expression with an algebraic identity to see if it's a square of a difference.

Now, let's work through each step:

Step 1: The given expression is $49 - 2 \times 21 + 9$. According to the order of operations, we will perform the multiplication first:

$2 \times 21 = 42$.

So, the expression becomes:

$49 - 42 + 9$.

Performing the subtraction gives us:

$49 - 42 = 7$.

Addition follows:

$7 + 9 = 16$.

Step 2: Now, we have to express 16 as a square of a difference. We find that:

$16 = (4)^2$.

Given the choices relate to squares of expressions in the form $(a-b)^2$, let's try expressing 16 as a square of the difference of two numbers:

The nearest choice is $(7-3)^2 = 7^2 - 2 \times 7 \times 3 + 3^2 = 49 - 42 + 9 = 16$.

Therefore, the simplified expression can be written as $(7-3)^2$.

Thus, the correct choice is $(7-3)^2$.