(x-y)^2 Formula Example

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

Understanding the (x-y)^2 Formula

The formula (x-y)^2 = x^2 - 2xy + y^2 is a fundamental algebraic concept used to expand the square of a binomial difference. Let's break down the formula and explore its practical applications.

What Does the Formula Mean?

The formula states that squaring a binomial difference (x-y) results in the sum of the square of the first term (x^2), minus twice the product of the first and second terms (2xy), plus the square of the second term (y^2).

Examples of the (x-y)^2 Formula

Let's illustrate this with a couple of examples:

Example 1:

  • Expand (a-b)^2

Using the formula, we get:

(a - b)^2 = a^2 - 2ab + b^2

Example 2:

  • Expand (2x - 3y)^2

Applying the formula, we have:

(2x - 3y)^2 = (2x)^2 - 2(2x)(3y) + (3y)^2 = 4x^2 - 12xy + 9y^2

Practical Applications of the (x-y)^2 Formula

This formula has various applications in algebra, geometry, and other areas of mathematics:

  • Simplifying expressions: It allows us to simplify algebraic expressions by expanding and combining terms.
  • Solving equations: The formula is useful in solving quadratic equations and other polynomial equations.
  • Geometric applications: The formula helps in calculating areas and volumes of geometric shapes.

Remember the Key Points

  • The formula applies to binomial differences, meaning two terms are subtracted.
  • The middle term of the expanded expression is always negative ( -2xy).
  • Practice using the formula with different examples to solidify your understanding.

The (x-y)^2 formula is a valuable tool in understanding and manipulating algebraic expressions. By mastering this formula, you will gain a deeper understanding of fundamental algebraic concepts.

Related Post