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The substitution method is a fundamental concept in mathematics that involves replacing variables with known values. This process is often used when evaluating algebraic expressions, as it allows us to determine the specific value of an expression when certain variables are assigned specific numbers. For example, if we have a polynomial expression and are given values for each variable, we can substitute these values into the expression.
When substituting, ensure the operations in the expression are carried out in their proper order by following the PEMDAS rule (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

• Identify the variables that need substitution.
• Replace each variable with the given number.
• Once values are replaced, simplify the expression using correct order of operations.

This method makes it easier to handle complex expressions and is a crucial step in solving or simplifying polynomials.

Polynomial simplification is the process of making a polynomial expression more concise and straightforward. After substituting the values of the variables in a polynomial, the next step is often to simplify the expression. This involves combining like terms and performing arithmetic operations. In the original exercise, once we substitute the values, \[(2)^2 + 3(2)(-3) + (-3)^2\]we proceed by simplification:

• The exponentiation is handled first: \((2)^2 = 4\) and \((-3)^2 = 9\).
• Then, we handle the multiplication: \(3 \times 2 \times (-3) = -18\).
• Finally, combine all terms: \(4 - 18 + 9 = -5\).

Therefore, polynomial simplification helps clarify the expression and reduces it to a single, understandable value.

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables, and operators. Understanding algebraic expressions is key to solving problems involving polynomials. They form the backbone of many mathematical disciplines.These expressions may comprise:

• Variables such as \(x\) and \(y\) which can take on different values.
• Constants which are fixed numerical values.
• Operators such as addition (+), subtraction (-), multiplication (*), and division (/).
• Exponents that denote repeated multiplication.

For example, in the polynomial \(x^2 + 3xy + y^2\), \(x\) and \(y\) are variables, while 3 is a constant coefficient applied to the term \(3xy\). Recognizing each part of an algebraic expression and understanding how they interact when combined can help in evaluating and simplifying such expressions.