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Algebraic expressions are combinations of variables, numbers, and operations. They form the building blocks of algebra. In the given exercise, the expression \( (a + 8)(a - 8) \) involves variables (\( a \)) and constants (\( 8 \)). Understanding how to manipulate these expressions is crucial.

Key features of algebraic expressions:

• They can include variables (e.g., \( x, y, a \)).
• They often contain constants (e.g., \( 3, 8, 12 \)).
• They use operations such as addition, subtraction, multiplication, and division.

Identifying the parts of an algebraic expression helps in simplifying and solving it step-by-step.

Polynomials are a specific type of algebraic expression that include multiple terms. Each term can be a constant, a variable, or a product of constants and variables raised to a power. For example, the expression \( a^2 - 64 \) is a polynomial with two terms.

Features of polynomials:

• They consist of one or more terms.
• Each term is separated by a plus or minus sign.
• They have variables raised to whole number exponents.

In the difference of squares formula, \( (a + b)(a - b) \) simplifies to a polynomial \( a^2 - b^2 \), making it easier to understand and use in problem-solving.

Factoring is the process of breaking down a complex expression into simpler components that, when multiplied together, give the original expression. In the given exercise, recognizing the difference of squares pattern allows us to use factoring to simplify \( (a + 8)(a - 8) \) into \( a^2 - 64 \).

Steps in factoring the difference of squares:

• Identify the form \( (a + b)(a - b) \).
• Apply the formula \( a^2 - b^2 \).
• Simplify the terms to get the final polynomial.

Factoring is a powerful tool in algebra for simplifying expressions and solving equations efficiently.