Understanding Like Terms in Mathematics

Like terms are used in mathematics to describe two or more expressions that have the same variable or variables with the same exponents. The expressions may also have different coefficients, which is the number that is multiplied by the variable. For example, 6x and 2x are like terms because they have the same variable, x, with a coefficient of 6 and 2 respectively. Knowing how to identify and combine like terms is an important part of algebra.

Applying Like Terms to 5a5b4

When looking at the expression 5a5b4, the first step is to identify the like terms. In this expression, 5a and 5b are like terms because they both have the same coefficients, 5, and the same variable, a and b. The 4 at the end of the expression is a constant because it is not multiplied by any variables.

Combining Like Terms

Once a student has identified the like terms in an expression, they can then combine them. In the expression 5a5b4, the like terms 5a and 5b can be combined to make 10ab. This is done by simply adding the coefficients together, giving 10ab. However, the constant cannot be combined with the like terms. Therefore, the expression 5a5b4 can be simplified to 10ab4.

Using Distributive Property

The distributive property is an algebraic property that states that when a number is multiplied by a group of numbers that are added or subtracted, the number can be distributed over each of the numbers in the group. This property can also be applied when combining like terms. For example, with the expression 5a5b4, the 5 can be distributed over 5a and 5b, giving 25ab4. This is the same result as combining the like terms, 10ab4.

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Like terms are used in mathematics to describe two or more expressions that have the same variable or variables with the same exponents. Knowing how to identify and combine like terms is an important part of algebra. When looking at the expression 5a5b4, the first step is to identify the like terms. 5a and 5b are like terms because they both have the same coefficients and the same variables. Once the like terms are identified, they can then be combined to make 10ab or the distributive property can be applied to give 25ab4.