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, expand each term by writing the products as sums. Use repeated addition to show 1 group of a, then 3 groups of b, then 4 groups of a, minus 2 groups of b.
1a+3b+4a−2b
( ) + ( + + ) + ( + + + ) - ( + )

Answer 1

To expand the expression \(1a + 3b + 4a - 2b\) using repeated addition, we can break it down step by step:

1. Start with \( 1a \):

   • This represents 1 group of \( a \): \((a)\)

2. Then for \( 3b \):

   • This represents 3 groups of \( b \): \((b + b + b)\)

3. Next, for \( 4a \):

   • This represents 4 groups of \( a \): \((a + a + a + a)\)

4. Finally, for \(-2b\):

   • This represents -2 groups of \( b \): \(-(b + b)\) or it can simply be expressed as \((-b - b)\)

Putting it all together, we have:

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

This can be organized as:

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

Overall, your expression can be written as:

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

Now, combine like terms:

• Total \( a \) terms: \( 1a + 4a = 5a \)
• Total \( b \) terms: \( 3b - 2b = 1b \)

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

\[ 5a + 1b \quad \text{or simply} \quad 5a + b \]