%5E2-answer.jpeg "(a+b+c)^2 Answer")
Expanding (a+b+c)^2: A Mathematical Exploration
In algebra, one of the most fundamental concepts is the expansion of binomials and polynomials. One such expression is (a+b+c)^2, which may seem daunting at first, but fear not! In this article, we will delve into the world of algebra and explore the steps to expand this expression.
The Formula
Before we dive into the expansion, let's first recall the formula for the square of a binomial:
(a + b)^2 = a^2 + 2ab + b^2
This formula can be extended to the square of a trinomial, which is what we're dealing with in this case.
Expanding (a+b+c)^2
To expand (a+b+c)^2, we can start by rewriting the expression as:
(a + (b + c))^2
Now, we can apply the formula for the square of a binomial, treating (b + c) as a single entity:
(a + (b + c))^2 = a^2 + 2a(b + c) + (b + c)^2
Next, we need to expand the term (b + c)^2. Using the same formula, we get:
(b + c)^2 = b^2 + 2bc + c^2
Substituting this back into our original expression, we get:
(a + (b + c))^2 = a^2 + 2a(b + c) + b^2 + 2bc + c^2
Simplifying the Expression
Now, let's simplify the expression by combining like terms:
(a + b + c)^2 = a^2 + 2ab + 2ac + b^2 + 2bc + c^2
And there you have it! We have successfully expanded the expression (a+b+c)^2.
Conclusion
In this article, we have seen how to expand the expression (a+b+c)^2 using the formula for the square of a binomial and some clever algebraic manipulations. This expansion can be useful in various mathematical derivations and applications. Remember, practice makes perfect, so be sure to try expanding other expressions on your own!
