2%3Da2%2B2ab%2Bb2-answer.jpeg "(a+b)2=a2+2ab+b2 Answer")
(a+b)² = a² + 2ab + b²: The Answer
What is (a+b)²?
The expression (a+b)² is a quadratic expression that is commonly encountered in algebra and geometry. It is a binomial expression that is raised to the power of 2. The expanded form of this expression is a topic of interest in mathematics, and it has many practical applications.
The Expansion
The expansion of (a+b)² is given by:
(a+b)² = a² + 2ab + b²
This expansion is a fundamental concept in algebra and is widely used in various mathematical calculations.
Proof of the Expansion
The proof of the expansion can be demonstrated using the distributive property of multiplication over addition. The expression (a+b)² can be written as:
(a+b)² = (a+b)(a+b)
Using the distributive property, we can expand the expression as:
(a+b)(a+b) = a(a+b) + b(a+b)
= a² + ab + ba + b²
= a² + 2ab + b²
Therefore, we have derived the expansion of (a+b)² as a² + 2ab + b².
Applications of the Expansion
The expansion of (a+b)² has numerous applications in various fields, including:
- Algebra: The expansion is used to simplify complex quadratic expressions and solve equations.
- Geometry: The expansion is used to calculate the area of rectangles and squares.
- Physics: The expansion is used to model real-world phenomena, such as the motion of objects.
- Engineering: The expansion is used to design and optimize systems, such as bridges and buildings.
Conclusion
In conclusion, the expansion of (a+b)² as a² + 2ab + b² is a fundamental concept in mathematics that has far-reaching applications in various fields. Understanding this expansion is crucial for problem-solving and critical thinking in mathematics.
