Factoring a Difference of Squares: Solve x^2 - 49 = (x-_—)(x+_—)

Fill in the missing element to obtain a true expression:

$x^2-49=(x-_—)\cdot(x+_—)$

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

• Step 1: Recognize that $49 = 7^2$.
• Step 2: Apply the difference of squares formula $a^2 - b^2 = (a - b)(a + b)$.
• Step 3: Compare the equation to the form and determine the blanks as $7$.

Now, let's work through each step:

Step 1: The given expression is $x^2 - 49$. Observe that 49 is a perfect square, written as $7^2$.

Step 2: According to the difference of squares formula, $x^2 - 49$ can be rewritten as $x^2 - 7^2$, which equals $(x - 7)(x + 7)$.

Step 3: Plugging in our values, we know the expression matches the form $(x - \_)\cdot(x + \_)$, with $7$ being the missing number.

Therefore, the solution to the problem is 7, which corresponds to choice 2.