"Using distributive, associative, or commutative property, prove that x^2 - 4 is equivalent to (x - 2)(x + 2)."

Firstly, which property would I use to solve this and show equivalence? Secondly, which steps would I need to take in order to show this/obtain my supposed answer ((x - 2)(x + 2)) from the given binomial (x^2 - 4)? I'm really strugglng with this. Thanks! :-)

This is the common equation (a-b)(a+b)= a^2 -b^2. You would use the distributive property

To prove that x^2 - 4 is equivalent to (x - 2)(x + 2), we can use the distributive property.

Step 1: Start with the expression x^2 - 4.
Step 2: Look for any common factors or patterns that can be applied.
Step 3: Notice that 4 is a perfect square (2^2). So, we can rewrite the expression as x^2 - 2^2.
Step 4: Now, we can apply the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b). In this case, a = x and b = 2.
Step 5: Using the difference of squares formula, we can rewrite x^2 - 2^2 as (x - 2)(x + 2).

Therefore, by applying the difference of squares formula, we have shown that x^2 - 4 is equivalent to (x - 2)(x + 2).