%E2%88%92(4x2%2B5x%E2%88%929)-adding-and-subtracting-polynomials.jpeg "(10x2−7x+7)−(4x2+5x−9) Adding And Subtracting Polynomials")
Adding and Subtracting Polynomials: A Step-by-Step Guide
This article will guide you through the process of adding and subtracting polynomials, using the example of:
(10x² − 7x + 7) − (4x² + 5x − 9)
Understanding Polynomials
A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial has a specific degree, which is the power of the variable in that term.
Example: In the polynomial (10x² − 7x + 7), the term 10x² has a degree of 2, -7x has a degree of 1, and 7 has a degree of 0 (because x⁰ = 1).
Adding Polynomials
To add polynomials, we simply combine like terms. Like terms are terms that have the same variable and the same degree.
Steps:
- Identify like terms.
- Add the coefficients of the like terms.
Example:
(10x² − 7x + 7) + (4x² + 5x − 9)
- x² terms: 10x² + 4x² = 14x²
- x terms: -7x + 5x = -2x
- Constant terms: 7 - 9 = -2
Therefore, the sum of the polynomials is: 14x² - 2x - 2
Subtracting Polynomials
Subtracting polynomials is similar to adding them, but we must first distribute the negative sign to the second polynomial.
Steps:
- Change the signs of all terms in the second polynomial.
- Combine like terms.
Example:
(10x² − 7x + 7) − (4x² + 5x − 9)
-
Distribute the negative sign: (10x² − 7x + 7) + (-4x² - 5x + 9)
-
Combine like terms:
- x² terms: 10x² - 4x² = 6x²
- x terms: -7x - 5x = -12x
- Constant terms: 7 + 9 = 16
Therefore, the difference of the polynomials is: 6x² - 12x + 16
Key Points to Remember
- When adding or subtracting polynomials, only like terms can be combined.
- Distribute the negative sign when subtracting polynomials.
- Simplify the expression by combining like terms.
By following these steps, you can successfully add and subtract polynomials and simplify complex expressions.