Question

M6|L20 Combining Like Terms (Part 1)Sign out
To start writing an equivalent expression, write the product 4b as a sum, using repeated addition.
3a + 4b + a +2b
=a + a + a + + + + + a+2b

Answer 1

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:

\[4a + 6b\]