Math Example--Polynomial Concepts--Adding and Subtracting Polynomials: Example 13

Topic

Polynomials

Description

Subtract the polynomials 2x³ + 4x² - 2x + 5 and 5x³ + 8x² + 2x + 15. Describe the difference of the polynomials.. Combine like terms and simplify: (2x³ - 5x³) + (4x² - 8x²) + (-2x - 2x) + (5 - 15) = -3x³ - 4x² - 4x - 10. The difference is a cubic polynomial.

The topic of Polynomials is central to algebra. Adding and subtracting polynomials allows students to practice combining like terms and understanding the structure of polynomial expressions. These examples demonstrate the systematic approach to organizing and combining terms.

Seeing multiple worked-out examples is crucial for students to develop a strong understanding of a concept. It allows them to recognize patterns, see commonalities, and build their problem-solving skills.

Teacher’s Script: Let's look at this example together. Notice how we identify and combine like terms. For example, when adding 2x and 5x, we first ensure they are like terms (both have the same variable and exponent). Then, we simply add their coefficients, resulting in 7x. In this two cubic expressions are combined into this cubic expression: -3x³ - 4x² - 4x - 10.

For a complete collection of math examples related to Polynomials click on this link: Math Examples: Adding and Subtracting Polynomials Collection.