Like Terms

Summary: Like terms are terms that are entirely the same with respect to their letters, so they may be combined into a single term during addition or subtraction. (source: chapter-1.2.1, source: chapter-1.2.2)

Sources: chapter-1.2.1, chapter-1.2.2

Last updated: 2026-04-26

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Definition

Euler says terms may be reduced together when they are “entirely the same with regard to letters.” In modern language, these are like terms. (source: chapter-1.2.1)

For example,

$$3a+2a=5a,-6c+10c=4c,-3d-5d=-8d.$$

(source: chapter-1.2.1)

Limits of Reduction

Terms that differ in their literal part cannot be combined into a single term. Euler gives examples such as $2a^2+3a$ and $2b^3-b^4$. (source: chapter-1.2.1)

Use in Subtraction

After signs are changed in subtraction, the result is reduced by the same rule for like terms used in addition. (source: chapter-1.2.2)

Related pages

• compound-quantities
• ch1.2.1-addition-compound-quantities
• ch1.2.2-subtraction-compound-quantities
• powers-and-exponents