Finding the Sum of Complex Polynomial Expressions

In high school mathematics, students often encounter the task of adding or subtracting algebraic expressions. This can become particularly challenging when dealing with complex polynomial expressions that involve multiple variables raised to different powers. In this article, we will walk through the process of finding the sum of two such expressions.

The two expressions we will be working with are:

1. x^3 y + x^2 y^2 - 3 x y^3
2. x^3 - 3 x^3 y + y^3 + 4 x y^3

To find the sum of these expressions, we will follow these steps:

1. Identify the like terms: The first step is to identify the terms in the two expressions that have the same variable factors, but with different exponents. In this case, the like terms are:

• x^3 y and -3 x^3 y
• x y^3 and 4 x y^3

1. Combine the like terms: Next, we will combine the like terms by adding the coefficients together. This gives us:

• x^3 y - 3 x^3 y = -2 x^3 y
• x y^3 + 4 x y^3 = 5 x y^3

1. Arrange the terms in the final expression: Now, we can arrange the terms in the final expression, grouping the like terms together:

• x^3 - 2 x^3 y + x^2 y^2 - 3 x y^3 + y^3 + 5 x y^3

1. Simplify the expression: The final step is to simplify the expression by combining the like terms. This gives us the final result:

• x^3 - 2 x^3 y + x^2 y^2 + 2 x y^3 + y^3

Therefore, the sum of the two original expressions is x^3 - 2 x^3 y + x^2 y^2 + 2 x y^3 + y^3.

This process of finding the sum of complex polynomial expressions is an essential skill in high school mathematics, as it helps students develop their understanding of algebraic operations and prepare for more advanced topics in calculus and beyond.