hằng đẳng thức

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The Vietnamese word "hằng đẳng thức" translates to "identity" in English, specifically in the context of mathematics. It refers to an equation that holds true for all values of the variables involved.

Explanation:

In mathematics, an identity is a statement that is always true, no matter what values the variables take. For example, the equation ( (a + b)^2 = a^2 + 2ab + b^2 ) is an identity because it is valid for any numbers ( a ) and ( b ).

Usage Instructions:

You can use "hằng đẳng thức" when discussing mathematical concepts, particularly in algebra, calculus, or any field where equations are involved. When you encounter an equation that is universally true, you can refer to it as a "hằng đẳng thức."

Example:

• A basic example is the identity:
  • ( x^2 - y^2 = (x - y)(x + y) )
  • This means that for any values of ( x ) and ( y ), this equation will always be true.

Advanced Usage:

In more advanced mathematics, "hằng đẳng thức" can be used to derive new equations or simplify expressions. Understanding identities is crucial for solving equations and proving other mathematical theorems.

Word Variants:

There are no direct variants of "hằng đẳng thức," but it can appear in different contexts or forms, such as: - "hằng đẳng thức lượng giác" (trigonometric identities) - "hằng đẳng thức đại số" (algebraic identities)

Different Meanings:

While "hằng đẳng thức" primarily refers to mathematical identities, in some contexts, it may also relate to the concept of invariance or consistency in other fields.

Synonyms:

In English, synonyms for "identity" in a mathematical sense include: - Equation (in specific contexts) - Formula (when referring to a standard mathematical relationship)

Summary:

The term "hằng đẳng thức" is essential for anyone studying mathematics in Vietnamese.

Academic

1. (toán) Identity