2-formula-answer.jpeg "(a-b)2 Formula Answer")
(a-b)² Formula: A Comprehensive Guide
The (a-b)² formula, also known as the difference of squares formula, is a fundamental concept in algebra and mathematics. It is used to expand the square of a binomial expression, which involves the subtraction of two terms. In this article, we will delve into the details of the (a-b)² formula, its derivation, examples, and applications.
What is the (a-b)² Formula?
The (a-b)² formula is a mathematical expression that represents the square of a binomial expression a-b. It is defined as:
(a-b)² = a² - 2ab + b²
This formula is used to expand the square of a binomial expression, which involves the subtraction of two terms. The formula is widely used in various mathematical operations, such as algebra, geometry, and calculus.
Derivation of the (a-b)² Formula
The (a-b)² formula can be derived by using the distributive property of multiplication over subtraction. Let's start with the binomial expression a-b and square it:
(a-b)² = (a-b) × (a-b)
Using the distributive property, we can expand the expression as:
(a-b) × (a-b) = a × a - a × b - b × a + b × b
Simplifying the expression, we get:
(a-b) × (a-b) = a² - 2ab + b²
Therefore, the (a-b)² formula is derived as:
(a-b)² = a² - 2ab + b²
Examples of the (a-b)² Formula
Here are some examples to illustrate the application of the (a-b)² formula:
Example 1:
Expand the expression (x-3)² using the (a-b)² formula.
(x-3)² = x² - 2 × x × 3 + 3² (x-3)² = x² - 6x + 9
Example 2:
Simplify the expression (2y-5)² using the (a-b)² formula.
(2y-5)² = (2y)² - 2 × 2y × 5 + 5² (2y-5)² = 4y² - 20y + 25
Applications of the (a-b)² Formula
The (a-b)² formula has numerous applications in various mathematical operations, including:
- Algebra: The formula is used to solve quadratic equations, simplify expressions, and factorize polynomials.
- Geometry: It is used to calculate the area and perimeter of geometric shapes, such as triangles and quadrilaterals.
- Calculus: The formula is used to solve optimization problems and find the maximum and minimum values of functions.
In conclusion, the (a-b)² formula is a fundamental concept in mathematics that has numerous applications in algebra, geometry, and calculus. Its derivation is based on the distributive property of multiplication over subtraction, and it is used to expand the square of a binomial expression.
