M6|L20 Combining Like Terms (Part 1)Sign out

Question

Write an equivalent expression with the fewest possible terms.
To start writing an equivalent expression, write the products as sums. Use repeated addition to show 4 groups of a, then 1 group of b, then 2 groups of a, then 2 groups of b.
4a+1b+2a+2b
( + + + ) + ( ) + ( + ) + ( + )

Answer 1

To write the expression \( 4a + 1b + 2a + 2b \) using repeated addition for each group, we can break it down as follows:

1. 4 groups of \( a \): \[ a + a + a + a \]

2. 1 group of \( b \): \[ b \]

3. 2 groups of \( a \): \[ a + a \]

4. 2 groups of \( b \): \[ b + b \]

Now, we can put it all together:

\[ (a + a + a + a) + (b) + (a + a) + (b + b) \]

Finally, to write the equivalent expression with the fewest possible terms, we combine like terms:

\[ (4a + 2a) + (1b + 2b) \]

This simplifies to:

\[ 6a + 3b \]

So the final equivalent expression with the fewest possible terms is:

\[ 6a + 3b \]