M6|L22 Combining Like Terms (Part 3)Sign out

Question

Write the expression in simplest form.
Use the distributive property to write an equivalent expression without parentheses.
(24c+3d)−(6c+15d)
= 24c + 3d +
+
You got it!
Next, write an equivalent expression by grouping all of the like variables together.
=
24c
+
−6c
+
3d
+
−15d
You got it!
Now write an equivalent expression with the fewest possible terms.
(24c+3d)−(6c+15d)
= 24c + 3d + −6c + −15d
= 24c + −6c + 3d + −15d
=
Great job!
Factor to rewrite the expression another way. To start factoring, choose the greatest common factor of 18c and −12d.
(24c+3d)−(6c+15d)
= 24c + 3d + −6c + −15d
= 24c + −6c + 3d + −15d
= 18c+−12d

6

7

5
You got it!
Now find the factors that, when multiplied by 6, equal 18c and −12d and fill them in the parentheses to write the factored expression.
(24c+3d)−(6c+15d)
= 24c + 3d + −6c + −15d
= 24c + −6c + 3d + −15d
= 18c+−12d
= 6(
+
)

Answer 1

Let's go through the steps as outlined and fill in the blanks.

1. Starting with the expression \((24c + 3d) - (6c + 15d)\):

   First, we distribute the negative sign:

   \[ = 24c + 3d - 6c - 15d \]

2. Next, we group like terms together:

   \[ = (24c - 6c) + (3d - 15d) \]

3. Simplifying the grouped terms gives:

   \[ = 18c - 12d \]

4. To factor out the greatest common factor (GCF) from \(18c\) and \(-12d\), we find that the GCF is \(6\).

   Therefore:

   \[ = 6(3c - 2d) \]

In summary, we can rewrite the original expression as follows:

\[ (24c + 3d) - (6c + 15d) = 6(3c - 2d) \]

So the filled-in expression is:

\[ 6(3c + (-2d)) \]

Thus, the complete factored form is:

\[ (24c + 3d) - (6c + 15d) = 6(3c - 2d) \]