(b%2Bc)(c%2Ba)-8abc.jpeg "(a+b)(b+c)(c+a) 8abc")
Expansion of (a+b)(b+c)(c+a) and its Simplification
In algebra, expanding and simplifying expressions is a crucial skill to master. In this article, we will explore the expansion of the expression (a+b)(b+c)(c+a) and simplify it to its simplest form.
Expanding the Expression
To expand the expression (a+b)(b+c)(c+a), we need to follow the order of operations (PEMDAS). First, we will expand the first two parentheses:
(a+b)(b+c) = ab + ac + bb + bc
Now, we will expand the resulting expression with the last parenthesis:
(ab + ac + bb + bc)(c+a) = ab(c+a) + ac(c+a) + bb(c+a) + bc(c+a)
Expanding each term, we get:
= abc + aba + acc + aca + bbc + bba + bcc + bca
Simplifying the Expression
Now, let's simplify the expression by combining like terms:
= abc + aba + acc + aca + bbc + bba + bcc + bca
= abc + abc + acc + acc + abc + abc + abc + abc
= 8abc
Thus, the simplified expression is 8abc.
In conclusion, we have successfully expanded and simplified the expression (a+b)(b+c)(c+a) to its simplest form, which is 8abc. This skill is essential in algebra and is used in various mathematical concepts, such as solving equations and inequalities, graphing functions, and more.
