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The difference of squares is an essential concept in algebra. It is a specific pattern used to simplify expressions where two terms are squared and subtracted. This pattern can be written as: \[ (a-b)(a+b) = a^2 - b^2 \].
In the example exercise, we have the binomials (3x-8) and (3x+8). This fits the difference of squares pattern with the terms \(a=3x\) and \(b=8\). By applying the formula, you simplify the product to find the final expression, which, in this case, is \(9x^2 - 64\).
The difference of squares formula makes it easier and quicker to solve problems involving products of binomials.

Binomial multiplication involves expanding expressions that contain two terms. The standard form for binomials is \((a+b)(c+d)\).
To multiply them, we use the distributive property (i.e., multiplying each term in the first binomial by each term in the second). However, in some cases, such as with the difference of squares, we can use specific formulas to simplify the process.
For our exercise, because the binomials (3x-8) and (3x+8) fit the difference of squares pattern, we can skip the usual steps of distributing and straight away apply the formula to arrive at the product. This way, instead of expanding \((3x-8)(3x+8)\) to \(3x(3x+8) - 8(3x+8)\), you directly write it as \((3x)^2 - 8^2 = 9x^2 - 64\).

Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. They are the building blocks of algebra and are used to represent real-world problems.
In the exercise provided, we deal with a specific kind of algebraic expression known as a binomial, which has two terms. Our binomials, (3x-8) and (3x+8), include both constants and variable terms.
Understanding how to manipulate and simplify these expressions using rules and formulas, like the difference of squares, is crucial for solving more complex algebra problems.
The final product of the binomials \((3x-8)(3x+8)\) simplifies to \(9x^2 - 64\) through these techniques, showcasing how we can handle algebraic expressions efficiently.