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When multiplying a square of a binomial like \( (x - 3)^2 \), we are essentially multiplying the binomial by itself, \( (x - 3)(x - 3) \). This is an important aspect of algebra that allows us to expand algebraic expressions. To multiply these binomials, we apply the FOIL method, which stands for First, Outer, Inner, Last. This refers to the terms in each binomial:

• First: Multiply the first terms of each binomial together (in this case \( x \times x \)),
• Outer: Multiply the outer terms ( \( x \times -3 \)),
• Inner: Multiply the inner terms ( \( -3 \times x \)),
• Last: Multiply the last terms of each binomial together ( \( -3 \times -3 \)).

After applying FOIL, combine like terms to arrive at the simplified expression \( x^2 - 6x + 9 \). Understanding this method allows us to tackle binomial multiplication with confidence.

Simplifying polynomials is a fundamental skill in algebra. It involves reducing the expression to its simplest form by combining like terms and performing any operations such as addition, subtraction, multiplication, and exponentiation.
To simplify the squared binomial \( (x - 3)^2 \), we first expand it to \( x^2 - 2x(3) + 3^2 \). We then multiply the terms where necessary, resulting in \( x^2 - 6x + 9 \). Here, there are no like terms to combine, so the simplified form remains \( x^2 - 6x + 9 \).

Understanding polynomial simplification is key to organizing and reducing expressions, making them easier to interpret and use in further calculations or applications.

Algebraic expressions are combinations of letters (variables) and numbers using mathematical operations. In the exercise \( (x - 3)^2 \), \( x \) is the variable and \( -3 \) is a constant number. When we square the binomial, we are raising the entire expression to the second power.

An expression like \( x^2 - 6x + 9 \) is a polynomial expression with three terms: \( x^2 \) is a quadratic term, \( -6x \) is a linear term, and \( 9 \) is a constant term. Familiarity with algebraic expressions is crucial to progress in algebra, as they are the building blocks for equations and functions which one will encounter in more advanced topics. Recognizing the structure of expressions helps in applying appropriate methods to simplify or solve them effectively.