The difference of squares refers to a specific algebraic identity that involves the subtraction of two squared terms. In this context, if we have a factor of x², we can represent the difference of squares as follows:
The general formula for the difference of squares is:
a² – b² = (a – b)(a + b)
Here, if we want to include a factor of x², we can express our terms accordingly. For example, let’s assume we have:
(x²)² – a²
This can be written as:
(x² – a)(x² + a)
So, if we complete the expression for a specific value of ‘a’, say if ‘a’ is ‘8’, we have:
(x² – 8)(x² + 8)
In summary, the difference of squares with a factor of x² results in factors that show how the square of a binomial can be broken down into simpler polynomial expressions. The calculations above help illustrate how you can explicitly see the difference by substituting values into the format provided.