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

Question

Write an equivalent expression with the fewest possible terms.
First, write subtraction as adding the opposite.
5a+1b−2a+3b
= 5a + 1b +
+ 3b

Answer 1

To combine the terms, we first convert the subtraction into addition by adding the opposite.

The expression is: \[ 5a + 1b - 2a + 3b \]

We can rewrite the subtraction as adding the opposite: \[ 5a + 1b + (-2a) + 3b \]

Now, group like terms:

1. Combine the \(a\) terms: \(5a - 2a = (5 - 2)a = 3a\)
2. Combine the \(b\) terms: \(1b + 3b = (1 + 3)b = 4b\)

Putting it all together, we get: \[ 3a + 4b \]

So, the equivalent expression with the fewest possible terms is: \[ 3a + 4b \]