Math Lesson 6.1.6 - Multiplying and Dividing Terms of an Algebraic Expression

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Welcome to our Math lesson on Multiplying and Dividing Terms of an Algebraic Expression, this is the sixth lesson of our suite of math lessons covering the topic of The Meaning of Expressions. Simplifying Expressions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Multiplying and Dividing Terms of an Algebraic Expression

If two or more terms of an algebraic expression are multiplied or divided, we make two different kinds of operations with their components. Thus, coefficients are multiplied or divided with each other according to the operation involved in the expression. As for the variable(s), from the two properties of exponents (indices)

and

it is clear that the total power of the same variable is obtained by adding or subtracting the individual powers. For example, if we have to calculate

Example 3

Simplify:

1. 18x² y³ ÷ 6xy + 5x² - 3y² - x² + 3y²
2. 5a - 3b² ∙ 2ab³ + 12ab⁶ ÷ 3b

Solution 3

1. Using the properties and rules explained so far, we obtain
   18x² y³ ÷ 6xy + 5x² - 3y² - x² + 3y²
   = (18 ÷ 6) x_{2 - 1} y_{3 - 1} + 5x² - 3y² - x² + 3y²
   = 3xy² + 5x² - 3y² - x² + 3y²
   = 5x² - x² + 3xy²- 3y² + 3y²
   = 4x² + 3xy² + 0y²
   = 4x² + 3xy²
2. Again, using the properties and rules explained so far, we obtain
   5a - 3b² ∙ 2ab³ + 12ab⁶ ÷ 3b
   = 5a - (3 ∙ 2) ab_{2 + 3} + (12 ÷ 3)ab_{6 - 1}
   = 5a - 6ab⁵ + 4ab⁵
   = 5a - 2ab⁵

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