%5E2-formula-proof.jpeg "(a+b)^2 Formula Proof")
(a+b)^2 Formula Proof
The (a+b)^2 formula is a well-known algebraic expression that is widely used in mathematics, particularly in algebra and geometry. In this article, we will provide a step-by-step proof of this formula.
What is the (a+b)^2 Formula?
The (a+b)^2 formula is a quadratic expression that represents the square of the sum of two variables, a and b. It is expressed as:
(a+b)^2 = a^2 + 2ab + b^2
Proof of the (a+b)^2 Formula
To prove this formula, we can use the distributive property of multiplication over addition, which states that:
(a+b)(a+b) = a(a+b) + b(a+b)
Step 1: Expand the Product
Using the distributive property, we can expand the product as:
(a+b)(a+b) = a^2 + ab + ba + b^2
Step 2: Combine Like Terms
Combine the like terms in the expanded product:
(a+b)(a+b) = a^2 + 2ab + b^2
Conclusion
Thus, we have successfully proved the (a+b)^2 formula:
(a+b)^2 = a^2 + 2ab + b^2
This formula is a fundamental concept in algebra and is used extensively in various mathematical derivations and applications.
