(a%2Bb)-is-equal-to.jpeg "(a-b)(a+b) Is Equal To")
(a-b)(a+b) is equal to
(a-b)(a+b) is a fundamental concept in algebra, and it's essential to understand its value. In this article, we'll explore the formula and its application.
The Formula
The formula for (a-b)(a+b) is:
(a-b)(a+b) = a^2 - b^2
This formula is widely used in various mathematical operations, such as simplifying expressions, solving equations, and manipulating algebraic expressions.
Proof
To prove the formula, let's start by multiplying the two binomials:
(a-b)(a+b) = a(a+b) - b(a+b)
Expanding the product, we get:
(a-b)(a+b) = a^2 + ab - ab - b^2
Combining like terms, we get:
(a-b)(a+b) = a^2 - b^2
Applications
The formula (a-b)(a+b) = a^2 - b^2 has numerous applications in mathematics, science, and engineering. Here are a few examples:
Simplifying Expressions
The formula can be used to simplify expressions involving the product of two binomials. For instance:
(x-2)(x+2) = x^2 - 4
Solving Equations
The formula can be used to solve quadratic equations of the form ax^2 + bx + c = 0. For example:
x^2 - 4 = 0
Using the formula, we can rewrite the equation as:
(x-2)(x+2) = 0
This simplifies to:
x - 2 = 0 or x + 2 = 0
Solving for x, we get:
x = 2 or x = -2
Geometry and Trigonometry
The formula has applications in geometry and trigonometry, particularly in calculating areas and volumes of shapes.
Conclusion
In conclusion, the formula (a-b)(a+b) = a^2 - b^2 is a fundamental concept in algebra, with numerous applications in mathematics, science, and engineering. Understanding this formula is essential for simplifying expressions, solving equations, and manipulating algebraic expressions.
