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
(
a
+
a
+
a
+
a
) + (
b
) + (
a
+
a
) + (
b
+
b
)
Nice!
Write another equivalent expression by grouping all of the like variables together.
4a+1b+2a+2b
( ) + ( ) + ( ) + ( )

Answer 1

To group all of the like variables together in the expression \(4a + 1b + 2a + 2b\), we can combine the terms that contain the same variable.

1. Combine like terms for \(a\):

   • \(4a + 2a = 6a\)

2. Combine like terms for \(b\):

   • \(1b + 2b = 3b\)

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

\[ 6a + 3b \]

In the grouping format, it would look like this:

\((a + a + a + a + a + a) + (b + b + b)\)

This indicates all the groups for \(a\) and \(b\) written out explicitly, which combines to give the simplified expression \(6a + 3b\).