(a+b)2 Answer

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Jul 03, 2024

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**(a+b)**²: The Formula and Its Applications

Introduction

The formula **(a+b)**² is a fundamental concept in algebra, and it has numerous applications in various fields of mathematics and science. In this article, we will explore the formula, its proof, and its applications.

The Formula

The formula **(a+b)**² is expressed as:

**(a+b)**² = a² + 2ab + b²

This formula is used to expand the square of a binomial expression, which is an expression consisting of two terms.

Proof

To prove this formula, let's start by expanding the square of (a+b):

**(a+b)**² = (a+b)(a+b)

= a(a+b) + b(a+b)

= a² + ab + ab + b²

= a² + 2ab + b²

Thus, we have derived the formula **(a+b)**² = a² + 2ab + b².

Applications

The formula **(a+b)**² has numerous applications in various fields, including:

Algebra

• Factoring: The formula is used to factor quadratic expressions, such as x² + 5x + 6.
• Solving Equations: It is used to solve quadratic equations, such as x² + 4x + 4 = 0.

Geometry

• Area of a Rectangle: The formula is used to find the area of a rectangle with sides (a+b) and (a-b).
• Perimeter of a Rectangle: It is used to find the perimeter of a rectangle with sides (a+b) and (a-b).

Physics

• Kinematics: The formula is used to calculate the distance traveled by an object under constant acceleration.
• Energy: It is used to calculate the kinetic energy of an object.

Conclusion

In conclusion, the formula **(a+b)**² is a powerful tool in algebra and has numerous applications in various fields of mathematics and science. It is essential to understand and apply this formula to solve problems and model real-world situations.