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Variables substitution is a fundamental step in algebra. When you are given an expression that contains variables, your first task is to replace these variables with the specific numbers provided in your problem. This technique allows you to evaluate the expression numerically.
Let's break it down using our example, where the expression is \(ac + bc\). You are given the values \(a = 3\), \(b = 8\), and \(c = 2\). The process involves substituting each of these values into the expression.
Simply change the \(a\) to 3, the \(b\) to 8, and the \(c\) to 2, transforming the expression into \(3 \cdot 2 + 8 \cdot 2\).

• Identify the variables in the expression.
• Substitute each variable with its corresponding value.

Performing this step correctly is crucial, as it sets the stage for the calculations that follow.

Once you have substituted the variables, your next step is to carry out the arithmetic operations within the expression.
Arithmetic operations include addition, subtraction, multiplication, and division. In our example, after substituting the variables, the expression becomes \(3 \cdot 2 + 8 \cdot 2\).
First, handle the multiplications: calculate \(3 \cdot 2\) and \(8 \cdot 2\). The results are 6 and 16, respectively. This simplifies the expression to \(6 + 16\).

• Carry out multiplications first, respecting the order of operations (PEMDAS/BODMAS).
• After multiplication, proceed with any remaining addition or subtraction.

Following these steps ensures the expression is simplified methodically and correctly.

Problem-solving in mathematics involves understanding and executing a sequence of steps to arrive at an answer. With the algebraic expression given to us, we've already substituted the variables and performed necessary arithmetic operations.
The final part of problem-solving is to combine all prior results to derive the solution. In our case, we reach the final step of adding the results from earlier multiplications: \(6 + 16\), which equals 22.

• Evaluate all components of the expression sequentially.
• Combine all parts accordingly to find the final answer.

Mathematical problem-solving is about following a logical approach to find answers. It is essential to perform substitutions and operations correctly, as one incorrect step can lead to errors in the solution.