91Ó°ÊÓ

Expression evaluation means calculating the value of an expression. This involves following a series of steps that may include substituting variables with their known values. In this exercise, you were given specific values for the variables: \(a = 2\), \(b = 4\), and \(c = -3\). The expression was \(2(3c+7)^{2}\). To evaluate the expression, you began by replacing \(c\) with \(-3\). This is crucial because it transforms an algebraic expression into a numerical one. While evaluating, you should follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Utilizing this order ensures that the expression is calculated correctly without errors.

Simplifying expressions involves reducing them to their simplest form by performing basic arithmetic operations and combining like terms. In our example, after substituting the variable \(c\) with \(-3\), the expression was transformed into \(2(3(-3) + 7)^{2}\). To simplify, you first dealt with the operation within the parentheses. Calculating \(3(-3) + 7\) meant you first did the multiplication, \(3  (-3) = -9\), followed by the addition, \(-9 + 7 = -2\). This simplified the portion inside the parentheses, helping to make the next steps of evaluating the expression easier. Simplifying expressions is an important skill because it helps in breaking down complex problems into simpler parts, making it easier to solve the equation accurately.

Parentheses indicate that the operations enclosed should be handled first. In our exercise, we encountered \(2(3 c+7)^{2}\). The parentheses were around \((3c + 7)\), which signifies that we must resolve this section before proceeding with any other calculation. Here are the steps you took:

• First, evaluate the expression inside the parentheses: \(3(-3) + 7\)
• This internal operation resulted in \(-2\).
• Next, address the exponent and any operations outside the parentheses.

Handling parentheses correctly is vital because it directs the order of operations in an expression, ensuring accuracy and meaning are preserved in calculations.