The difference of squares is a special algebraic expression that can be represented in the form of a² – b², which factors into (a + b)(a – b). When we consider the expression x², we can think about how to express it in terms of a difference of squares.
To complete the expression for a difference of squares involving x², we can set it up as follows:
- a = x
- b = k
Now, substituting into our difference of squares formula, we have:
x² – k² = (x + k)(x – k)
This means that any expression of the form x² – k² has x² as one of its components and is expressible as the product of (x + k) and (x – k).
For example, if we take a specific case where k equals 3, we would have:
x² – 3² = (x + 3)(x – 3)
In summary, the difference of squares involving x² represents an algebraic identity that demonstrates a relationship between two squares, effectively allowing us to factor expressions and find roots more efficiently. This approach is widely useful in algebra for solving quadratic equations or simplifying polynomial expressions.