%5E2-formula-example.jpeg "(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.