Exploring Like Terms in Mathematics: Definition, Examples, and Importance

Like terms

In mathematics, like terms refer to terms that have the same variable(s) raised to the same power(s)

In mathematics, like terms refer to terms that have the same variable(s) raised to the same power(s). In other words, like terms have the same combination of variables and exponents.

For example, consider the following algebraic expressions:

3x^2, -2x^2, and 5x^2

In this case, all three terms have the variable x raised to the power of 2. Therefore, these terms are considered like terms.

Now, let’s take another example:

2x^3, -5x^2, and 4x

Here, we have three terms, but the variable x is raised to different powers in each term. The first term has x raised to the power of 3, the second term has x raised to the power of 2, and the third term has x raised to the power of 1. Since the powers are different, these terms are not considered like terms.

To combine or simplify like terms, we add or subtract their coefficients (the numbers in front of the variable). The variable and its exponent remain the same.

For instance, if we are asked to simplify the expression:

3x^2 – 2x^2 + 5x^2

Since all three terms have x raised to the power of 2, we can combine them by adding their coefficients:

3x^2 – 2x^2 + 5x^2 = (3 – 2 + 5)x^2 = 6x^2

The result is 6x^2, with like terms being combined.

It is important to note that when simplifying expressions, we only combine terms that are like terms. Terms that have different variables or exponents cannot be combined.

Understanding like terms is crucial in various areas of mathematics, particularly in simplifying algebraic expressions and solving equations. By identifying like terms and combining them, we can make problems more manageable and find solutions efficiently.

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