2-formula-proof.jpeg "(a+b)2 Formula Proof")
The Proof of (a+b)^2 Formula
The formula (a+b)^2 = a^2 + 2ab + b^2 is a fundamental concept in algebra, and it has numerous applications in various branches of mathematics and science. In this article, we will provide a step-by-step proof of this formula.
The Formula
The formula (a+b)^2 is known as the "square of a binomial" formula, where a and b are two variables or constants.
(a+b)^2 = a^2 + 2ab + b^2
The Proof
To prove this formula, we will start with the left-hand side of the equation, which is (a+b)^2.
(a+b)^2 = (a+b)(a+b)
Using the distributive property of multiplication over addition, we can expand the right-hand side of the equation as follows:
(a+b)(a+b) = a(a+b) + b(a+b)
Now, we will expand each term on the right-hand side of the equation:
a(a+b) = a^2 + ab
b(a+b) = ab + b^2
Substituting these two expressions back into the original equation, we get:
(a+b)^2 = a^2 + ab + ab + b^2
Combining like terms, we finally arrive at the desired formula:
(a+b)^2 = a^2 + 2ab + b^2
Conclusion
In this article, we have provided a step-by-step proof of the (a+b)^2 formula. This formula is a fundamental concept in algebra and has numerous applications in various branches of mathematics and science. By understanding the proof of this formula, we can gain a deeper appreciation for the underlying principles of algebra and mathematics.
