To express the product \(4b\) as a sum using repeated addition, you would write:
\[4b = b + b + b + b\]
Now, incorporating that into the expression \(3a + 4b + a + 2b\):
Starting with:
\[3a + 4b + a + 2b\]
You can rewrite \(4b\) as \(b + b + b + b\) and \(2b\) as \(b + b\):
So, the expression becomes:
\[3a + (b + b + b + b) + a + (b + b)\]
Now, we can rearrange the terms for clarity:
\[3a + a + b + b + b + b + b + b\]
Combining like terms, we gather the \(a\) terms and the \(b\) terms:
- For the \(a\) terms: \(3a + a = 4a\)
- For the \(b\) terms: \(b + b + b + b + b + b = 6b\)
Therefore, the final combined expression is:
\[4a + 6b\]