(x-y)^2 Expand

3 min read Jun 17, 2024
(x-y)^2 Expand

Understanding the Expansion of (x-y)²

The expression (x-y)² represents the square of the binomial (x-y). Expanding this expression is a fundamental concept in algebra and is essential for various mathematical operations.

Understanding the Concept

The square of a binomial means multiplying the binomial by itself. Therefore:

(x - y)² = (x - y) * (x - y)

To expand this, we need to distribute each term of the first binomial to each term of the second binomial.

The Expansion Process

  1. Multiply the first terms: x * x = x²
  2. Multiply the outer terms: x * -y = -xy
  3. Multiply the inner terms: -y * x = -xy
  4. Multiply the last terms: -y * -y = y²

Now, we have: x² - xy - xy + y²

Simplifying the Expression

Combining like terms, we get the final expanded form:

(x - y)² = x² - 2xy + y²

Key Points to Remember

  • The sign of the middle term is always negative because the product of a positive and a negative term is negative.
  • The coefficient of the middle term is always twice the product of the two terms in the binomial.
  • The expansion of (x-y)² is a perfect square trinomial, meaning it can be factored back into the original binomial.

Applications of the Expansion

The expansion of (x-y)² is used extensively in:

  • Factoring polynomials: Knowing this expansion helps recognize and factor perfect square trinomials.
  • Solving equations: The expansion can be used to simplify equations involving squared binomials.
  • Calculus: Derivatives and integrals often involve expanding binomials.
  • Geometry: The expansion is used to derive formulas for areas and volumes of geometric shapes.


Understanding the expansion of (x-y)² is essential for a strong foundation in algebra. It allows for efficient manipulation of expressions, simplifying equations, and applying mathematical concepts in various fields.

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