2-formula-solution.jpeg "(a+b)2 Formula Solution")
(a+b)^2 Formula Solution
The (a+b)^2 formula, also known as the binomial squared formula, is a fundamental concept in algebra and is widely used in various mathematical operations. In this article, we will discuss the formula, its derivation, and provide examples to illustrate its application.
The Formula
The (a+b)^2 formula is given by:
(a+b)^2 = a^2 + 2ab + b^2
This formula allows us to expand the square of a binomial expression, which is an expression consisting of two terms.
Derivation
To derive the (a+b)^2 formula, we can start with the distributive property of multiplication over addition, which states that:
(a+b)(a+b) = a(a+b) + b(a+b)
Expanding the right-hand side of the equation, we get:
(a+b)(a+b) = a^2 + ab + ab + b^2
Combining like terms, we get the final formula:
(a+b)^2 = a^2 + 2ab + b^2
Examples
Example 1
Find the value of (x+3)^2.
Using the (a+b)^2 formula, we get:
(x+3)^2 = x^2 + 2(x)(3) + 3^2 (x+3)^2 = x^2 + 6x + 9
Example 2
Find the value of (2x-4)^2.
Using the (a+b)^2 formula, we get:
(2x-4)^2 = (2x)^2 + 2(2x)(-4) + (-4)^2 (2x-4)^2 = 4x^2 - 16x + 16
Importance and Applications
The (a+b)^2 formula has numerous applications in various branches of mathematics, including:
- Algebra: The formula is used to expand binomial expressions and to solve quadratic equations.
- Geometry: The formula is used to find the area of a square and to solve problems involving right triangles.
- Calculus: The formula is used to find the derivative and integral of functions.
In conclusion, the (a+b)^2 formula is a powerful tool in algebra and is widely used in various mathematical operations. Understanding the formula and its application is essential for students and professionals in the field of mathematics.
