Recognizing and Combining Like Terms in Mathematics | An Essential Step for Simplifying Algebraic Expressions and Solving Equations

like terms

In mathematics, like terms refer to terms that have identical variables raised to the same power

In mathematics, like terms refer to terms that have identical variables raised to the same power. Like terms can be combined or simplified by adding or subtracting them together.

For instance, consider the terms 3x and -2x. Here, both terms have the variable x raised to the first power. Since the variables and their exponents are the same, these terms are considered like terms.

Similarly, the terms 5y^2 and -2y^2 are like terms because they have the variable y raised to the second power.

On the other hand, terms such as 4x^2 and 3xy do not qualify as like terms. They have different variables (x and y) and different exponents (x^2 and xy) and cannot be combined in their current form.

When simplifying expressions or equations, collecting like terms is an important step to reduce the complexity and find the simplest form. By combining like terms and performing the associated operations, such as addition or subtraction, the expression or equation can be simplified to its most concise form.

For example, if we have the expression 2x – 3y + 5x + 4y, we can identify that 2x and 5x are like terms, and likewise, -3y and 4y are like terms. Combining these like terms, we get (2x + 5x) – (3y + 4y) = 7x – 7y as the simplified expression.

In summary, like terms are terms with the same variables raised to the same power. Recognizing and combining like terms is crucial for simplifying algebraic expressions and solving equations.

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