Completing the Expression: Find the Missing Numbers in x^2-36=(x-__)(__+x)

Fill in the missing element to obtain a true expression:

$x^2-36=(x-_—)\cdot(_—+x)$

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

• Step 1: Identify the given expression and recognize the form.
• Step 2: Apply the difference of squares formula.
• Step 3: Determine the missing element.
• Step 4: Verify the solution against the possible choices.

Now, let's work through each step:
Step 1: The given expression is $x^2 - 36$. This resembles a difference of squares, which is $a^2 - b^2$.
Step 2: Recognize that $x^2$ represents $a^2$ and $36$ represents $b^2$.
Step 3: Find $b$ such that $b^2 = 36$. This gives $b = 6$ because $6^2 = 36$.
Step 4: The difference of squares formula states $a^2 - b^2 = (a - b)(a + b)$. So we rewrite $x^2 - 36$ as $(x - 6)(x + 6)$.

Therefore, the missing element that makes the expression true is $6$.