%5E2-formula-expansion.jpeg "(a-b+c)^2 Formula Expansion")
Expanding (a - b + c)^2
The formula (a - b + c)^2 is a common algebraic expression that can be expanded using the principles of binomial expansion and the distributive property. Let's break down how to expand this expression.
Understanding the Formula
The formula (a - b + c)^2 essentially represents squaring the entire expression (a - b + c) which means multiplying it by itself:
(a - b + c)^2 = (a - b + c) * (a - b + c)
Expanding the Expression
To expand this, we need to distribute each term in the first expression with each term in the second expression. This can be visualized as follows:
(a - b + c)
* (a - b + c)
-------------------
a^2 - ab + ac
-ab + b^2 - bc
+ac - bc + c^2
-------------------
a^2 - 2ab + 2ac + b^2 - 2bc + c^2
Final Formula
By combining like terms, we arrive at the expanded formula:
(a - b + c)^2 = a^2 - 2ab + 2ac + b^2 - 2bc + c^2
Key Points
- Remember: The formula applies to any values of a, b, and c.
- Simplify: Make sure to combine like terms for the final result.
- Practice: Expanding similar expressions will help you understand the process and remember the formula.
This expansion is crucial for simplifying algebraic expressions and solving equations. Understanding the formula allows you to manipulate equations and solve for unknown variables.