What is the difference of squares formula?

The difference of squares formula is a fundamental identity in algebra that allows us to factor expressions of the form (a^2 - b^2). The correct formulation of this identity is (a^2 - b^2 = (a - b)(a + b)). This means that when you have a squared term subtracted from another squared term, you can express it as the product of the sum and the difference of the two terms, (a) and (b).

To understand why this is valid, consider that when you expand the right side, ((a - b)(a + b)), using the distributive property (also known as the FOIL method for binomials), you get:

1. (a \cdot a = a^2)

2. (a \cdot b = ab)

3. (-b \cdot a = -ab)

4. (-b \cdot b = -b^2)

When you combine these terms, the (ab) and (-ab) cancel each other out, leaving you with (a^2 - b^2). This demonstrates that the formula is indeed correct.

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