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
(
a + a + a + a
) + (
a + a
) + (
b + b
) + (
b
)
Good work!
Now, write another equivalent expression using the fewest possible terms.
4a+1b+2a+2b
= ( a + a + a + a ) + ( b ) + ( a + a ) + ( b + b )
= ( a + a + a + a ) + ( a + a ) + ( b ) + ( b + b )
=

Answer 1

To combine the like terms and simplify the expression \(4a + 1b + 2a + 2b\), we can follow these steps:

1. Identify the like terms:

   • For the variable \(a\): \(4a + 2a\)
   • For the variable \(b\): \(1b + 2b\)

2. Combine the like terms:

   • \(4a + 2a = 6a\)
   • \(1b + 2b = 3b\)

3. Write the equivalent expression using the fewest possible terms: \[ 6a + 3b \]

Therefore, the final simplified expression is: \[ 6a + 3b \]