Math Lesson 6.1.5 - Ordering the Terms of Algebraic Expressions

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Welcome to our Math lesson on Ordering the Terms of Algebraic Expressions, this is the fifth 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.

Ordering the Terms of Algebraic Expressions

In order to have a better understanding of an algebraic expression, it is better to have it expressed from the highest to the lowest term. The highest term of an expression is determined by the variable with the highest power. If two terms have the same power degree, we order them according the alphabet.

For example, the final expression of the previous paragraph

is normally written as

Example 2

Write the following algebraic expressions in the correct way.

1. 2 - 5y² + 3x + 6x² - 4x + y² - 2x²
2. 5x² y - 4y² + 2x - 3y - 6y² - 2x + 3x² y

Solution 2

1. We have four different sets of like terms in this expression: terms that involve x², y², x, and numbers. Completing operations (addition & subtraction) with the like terms, yields:
   2 - 5y² + 3x + 6x² - 4x + y² - 2x²
   = 6x² - 2x² - 5y² + y² + 3x - 4x + 2
   = 4x² - 4y² - x + 2
2. We have five different sets of like terms in this expression: terms that involve y², x, y, x²y and numbers. Completing operations (addition & subtraction) with the like terms, yields:
   5x² y - 4y² + 2x - 3y - 6y² - 2x + 3x² y
   = 5x² y + 3x² y - 4y² - 6y² + 2x - 2x - 3y
   = 8x² y - 10y² + 0x - 3y
   = 8x² y - 10y² - 3y

As you see, the terms involving the variable x cancel out as they have opposite coefficients (2 and -2), so they give zero when added.

Remark! It is more appropriate to write an algebraic expression containing two variables x and y in a way that the power of the first variable x decreases when moving from left to right while the power of the second variable y increases when moving from left to right. As for the constant, it is written at the end of the algebraic expression, after you have finished with all variables. For example, the final form of the first expression in the previous example is written as

and the final form of the second expression is written as

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