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Polynomial factoring is a process in algebra that involves breaking down a polynomial into simpler components called factors. These factors, when multiplied together, give back the original polynomial. Factoring can reveal more about the behavior of the polynomial, making it easier to solve equations and understand their properties.
To factor a polynomial, look for common factors among terms or recognize patterns such as the difference of squares, perfect square trinomials, or the sum/difference of cubes.
For instance, in our exercise, the polynomial is 9w^2 - 9n^2. This can be broken down by identifying common patterns such as the difference of squares, enabling us to easily factorize the polynomial.

The difference of squares formula is a handy tool in polynomial factoring. This formula applies to polynomials that can be expressed in the form of a^2 - b^2. The formula is written as:
a^2 - b^2 = (a - b)(a + b)
The difference of squares is recognizable because it consists of two squared terms separated by a subtraction sign ( - ).
In the exercise, we identified 9w^2 - 9n^2 as a difference of squares by expressing each term as squares:
9w^2 = (3w)^2
9n^2 = (3n)^2
Substitute these into the formula, where a = 3w and b = 3n, gives us:
(3w)^2 - (3n)^2 = (3w - 3n)(3w + 3n)
Through this formula, the polynomial 9w^2 - 9n^2 is factored into (3w - 3n)(3w + 3n).

Algebraic expressions are combinations of numbers, variables, and operations that represent a value or a relationship. Unlike equations, they don't have an equal sign. Algebraic expressions can be simplified, added, subtracted, factored, and more.
An important aspect of working with algebraic expressions is the ability to recognize patterns and use algebraic identities, like the difference of squares. This simplifies complex expressions and makes solving related equations straightforward.
In the exercise, we worked with the algebraic expression 9w^2 - 9n^2. By applying the difference of squares formula, we transformed it into a product of simpler factors: (3w - 3n)(3w + 3n). Understanding how to manipulate algebraic expressions helps in many areas of mathematics including solving equations, analyzing functions, and more.