Let's factor the given expression [tex]\(a^2bc + ab^2c + abc^2\)[/tex] step-by-step.
1. Identify the common factors:
Each term in the expression [tex]\(a^2bc + ab^2c + abc^2\)[/tex] shares some common factors. We observe that each term contains the factors [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
2. Factor out the common term:
Since [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are common to all terms, we can factor [tex]\(abc\)[/tex] from each term:
[tex]\[
a^2bc + ab^2c + abc^2 = abc \cdot a + abc \cdot b + abc \cdot c
\][/tex]
3. Rewrite the expression:
Factoring [tex]\(abc\)[/tex] out of the original expression, we get:
[tex]\[
abc (a) + abc (b) + abc (c)
\][/tex]
4. Combine the terms inside the parentheses:
Now we combine the terms inside the parentheses:
[tex]\[
abc (a + b + c)
\][/tex]
Therefore, the factored form of the expression [tex]\(a^2bc + ab^2c + abc^2\)[/tex] is [tex]\[\boxed{abc (a + b + c)}\][/tex].
