Which polynomial correctly combines the like terms embarks on an intellectual odyssey, unraveling the intricacies of polynomial expressions and the art of combining like terms. This discourse delves into the fundamental concepts, rules, and applications of this mathematical operation, empowering readers with a comprehensive understanding of this essential algebraic skill.
Like terms, the building blocks of polynomials, share identical variable factors raised to the same exponents. Identifying and combining these like terms simplifies polynomials, revealing their underlying structure and facilitating further mathematical operations.
Introduction: Which Polynomial Correctly Combines The Like Terms
In mathematics, a polynomial is an expression consisting of variables and constants, combined using mathematical operations such as addition, subtraction, multiplication, and exponents. Like terms in a polynomial are terms that have the same variables raised to the same powers.
Combining like terms involves adding or subtracting the coefficients of like terms to simplify the polynomial.
Identifying Like Terms
Like terms share the same variables raised to the same powers. For example, 3x^2 and 5x^2 are like terms, as are -4y and 2y. Non-like terms have different variables or different powers of the same variable. For example, 2x and 3y are not like terms, and neither are x^2 and x^3.
Rules for Identifying Like Terms, Which polynomial correctly combines the like terms
- Variables must be identical.
- Exponents on variables must be identical.
- Coefficients may be different.
Combining Like Terms
To combine like terms, add or subtract their coefficients while keeping the same variable and exponent. For example, 3x^2 + 5x^2 = 8x^2, and -4y – 2y = -6y.
Simplifying Polynomials
Combining like terms simplifies polynomials by reducing the number of terms. For example, the polynomial 2x^2 + 3x – 5x + 1 can be simplified by combining like terms to obtain 2x^2 – 2x + 1.
Applications
Combining like terms is used in various fields, including:
- Algebra
- Calculus
- Physics
- Engineering
Clarifying Questions
What are like terms?
Like terms are terms within a polynomial that have identical variable factors raised to the same exponents.
How do you combine like terms?
To combine like terms, add or subtract their coefficients while maintaining the same variable factors and exponents.
Why is combining like terms important?
Combining like terms simplifies polynomials, making them easier to analyze and manipulate for further mathematical operations.
