Understanding the (a+b+c)(a+bc) Formula
The formula (a+b+c)(a+bc) is a useful algebraic expression that can be simplified to a more compact form. This formula is often used in various mathematical problems, particularly in algebra and geometry.
Expanding the Formula
The formula can be expanded using the distributive property of multiplication. Let's break down the steps:

Multiply the first term of the first expression with each term of the second expression:
 a(a+bc) = a² + ab  ac

Multiply the second term of the first expression with each term of the second expression:
 b(a+bc) = ab + b²  bc

Multiply the third term of the first expression with each term of the second expression:
 c(a+bc) = ac + bc  c²

Add all the resulting terms together:
 a² + ab  ac + ab + b²  bc + ac + bc  c²

Combine like terms:
 a² + 2ab + b²  c²
The Simplified Formula
Therefore, the simplified form of the formula (a+b+c)(a+bc) is a² + 2ab + b²  c².
Applications of the Formula
This formula has several applications, including:
 Factoring expressions: The formula can be used to factor expressions in the form of a² + 2ab + b²  c².
 Solving equations: The formula can be used to solve equations that involve terms like (a+b+c)(a+bc).
 Geometric problems: The formula can be applied to find the area or volume of certain geometric shapes.
Conclusion
Understanding the (a+b+c)(a+bc) formula and its simplified form is essential for solving various mathematical problems. The formula is a powerful tool that can be used to simplify expressions, solve equations, and solve geometric problems.