%5E2-formula-class-9.jpeg "(x-y)^2 Formula Class 9")
Squares of Algebraic Expressions: (x-y)^2 Formula for Class 9
In Algebra, square of an algebraic expression is a fundamental concept that is used extensively in various mathematical operations. One such expression is (x-y)^2, which is a crucial formula that is used to simplify complex algebraic expressions. In this article, we will explore the (x-y)^2 formula, its derivation, and examples to illustrate its application.
Derivation of (x-y)^2 Formula
To derive the (x-y)^2 formula, we can start with the definition of square of an algebraic expression:
(x-y)^2 = (x-y) × (x-y)
Using the distributive property of multiplication over subtraction, we can expand the expression as:
(x-y)^2 = x^2 - xy - xy + y^2
Combine like terms to get:
(x-y)^2 = x^2 - 2xy + y^2
This is the (x-y)^2 formula.
Examples to Illustrate (x-y)^2 Formula
Example 1:
Expand (a-b)^2 using the formula.
(a-b)^2 = a^2 - 2ab + b^2
Example 2:
Simplify (2x-3y)^2 using the formula.
(2x-3y)^2 = (2x)^2 - 2(2x)(3y) + (3y)^2 (2x-3y)^2 = 4x^2 - 12xy + 9y^2
Example 3:
Find the value of (x-1)^2 when x = 4.
(x-1)^2 = x^2 - 2x + 1 (4-1)^2 = 4^2 - 2(4) + 1 (4-1)^2 = 16 - 8 + 1 (4-1)^2 = 9
Importance of (x-y)^2 Formula
The (x-y)^2 formula is used in various mathematical operations, such as:
- Algebraic Simplification: To simplify complex algebraic expressions, we can use the (x-y)^2 formula to expand and simplify the expression.
- Quadratic Equations: The formula is used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants.
- Geometry and Trigonometry: The (x-y)^2 formula is used to find the distance between two points in a coordinate plane, and in trigonometric identities.
In conclusion, the (x-y)^2 formula is an essential concept in Algebra that is used to simplify complex algebraic expressions and solve quadratic equations. By mastering this formula, students can develop their problem-solving skills and prepare themselves for advanced mathematical concepts.
