(a%2Bb)-answer.jpeg "(a-b)(a+b) Answer")
Algebraic Expansion: (a-b)(a+b) Answer
In algebra, expanding expressions involving binomials is a crucial skill to master. One of the most popular and useful expansions is the product of (a-b) and (a+b). In this article, we'll explore the answer to this expansion and its significance in mathematics.
The Expansion
The expansion of (a-b)(a+b) can be calculated by multiplying each term in the first binomial with each term in the second binomial. Using the distributive property of multiplication over addition, we get:
(a-b)(a+b) = a(a+b) - b(a+b)
= a^2 + ab - ba - b^2
Simplifying the Expression
Notice that the middle terms, ab and -ba, are opposites that cancel each other out. This leaves us with:
(a-b)(a+b) = a^2 - b^2
This simplified expression is a difference of squares, a fundamental concept in algebra.
Importance of (a-b)(a+b) Expansion
The expansion of (a-b)(a+b) has numerous applications in various mathematical areas, including:
1. Factoring Quadratic Expressions
The expansion can be used to factor quadratic expressions of the form x^2 + bx + c, where b and c are constants.
2. Solving Quadratic Equations
The difference of squares formula enables us to solve quadratic equations by finding the roots of the equation.
3. Geometry and Trigonometry
The expansion is used in geometric and trigonometric identities, such as the Pythagorean identity and the sum and difference formulas for sine, cosine, and tangent.
Conclusion
In conclusion, the expansion of (a-b)(a+b) is a fundamental concept in algebra, leading to the difference of squares formula, a^2 - b^2. This expansion has far-reaching implications in various areas of mathematics, making it an essential tool for problem-solving and critical thinking.
