Solving for x2y - y2 with Given Values: A Step-by-Step Guide

In this article, we provide a comprehensive guide on how to solve the algebraic expression x2y - y2 when given specific values for x and y. This process involves substituting the given values into the expression and then performing the necessary calculations in accordance with the order of operations (PEMDAS).

Given Values and Substitution

Let's start by understanding the given expression: x2y - y2. For this example, we are given the values x 3 and y 2. The first step is to substitute these values into the expression:

Substituting these values, the expression becomes:

32 * 2 - 22

Step-by-Step Calculation

Let's break down the calculation step by step:

1. Calculate x2

To calculate x2 when x 3:

x2 32 9

2. Calculate y2

To calculate y2 when y 2:

y2 22 4

3. Substitute x2 and y into the expression

Substitute the values of x2 and y back into the expression:

32 * 2 - 22 9 * 2 - 4

This simplifies to:

9 * 2 - 4

4. Perform Multiplication

According to the order of operations (PEMDAS), perform the multiplication first:

9 * 2 18

5. Perform Subtraction

Now, subtract y2 (which is 4) from the result of the multiplication:

18 - 4 14

Conclusion

Therefore, the value of the expression x2y - y2 when x 3 and y 2 is 14.

Note: The initial computation given in the example (resulting in 20) seems to have an error. Applying the correct order of operations and substituting the values correctly, the result is indeed 14, not 22.

Understanding the order of operations (PEMDAS) and substituting given values into algebraic expressions is crucial for solving such problems accurately. This guide should help in grasping the process and ensuring correct calculations.