LIKE TERMS Meaning and
Definition
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Like terms refer to algebraic terms or expressions that have the same variables or variables with the same exponents. Like terms are essential in algebraic simplification and combining them simplifies mathematical expressions by allowing similar terms to be grouped together. These terms can be added or subtracted from each other.
To determine if two terms are like terms, one must examine the variables and their exponents. If the variables in both terms are the same and have the same exponent, they are considered like terms. For example, "3x" and "2x" are like terms because they both have the variable "x" raised to the first power. Another example is "4y^2" and "5y^2," since both terms have the variable "y" raised to the second power.
Unlike terms, on the other hand, do not have the same variables or variables with the same exponents. For instance, "3x" and "2y" are unlike terms because the variables are different. Similarly, "4x^2" and "5x" are unlike terms because the exponents differ.
Combining like terms involves adding or subtracting their coefficients while keeping the variables and their exponents the same. This simplification allows manipulations of algebraic expressions, such as factoring or solving equations. By grouping like terms, algebraic expressions become more manageable and easier to solve, ultimately leading to a clearer understanding of mathematical relationships and operations.
Etymology of LIKE TERMS
The term "like terms" is a mathematical concept rather than a word with etymology. In mathematics, like terms refer to terms that have the same variables raised to the same powers. For example, in the equation 3x + 2y + 5x - 4y, the terms 3x and 5x are like terms because they both have the variable x raised to the power of 1. Likewise, the terms 2y and -4y are like terms as they both have the variable y raised to the power of 1.
