Certainly! Let's simplify the given mathematical expression step-by-step.
Given expression:
[tex]\[
(16bc - 12cd) + (8cd - 6bc + 4bd)
\][/tex]
### Step 1: Remove the parentheses
First, we'll remove the parentheses in the expression:
[tex]\[
16bc - 12cd + 8cd - 6bc + 4bd
\][/tex]
### Step 2: Combine like terms
Next, we identify and combine the like terms. Like terms are terms that contain the same variables raised to the same power.
The terms involving [tex]\(bc\)[/tex] are:
[tex]\[
16bc - 6bc
\][/tex]
The terms involving [tex]\(cd\)[/tex] are:
[tex]\[
-12cd + 8cd
\][/tex]
And the term involving [tex]\(bd\)[/tex] is:
[tex]\[
4bd
\][/tex]
### Step 3: Perform the arithmetic operations on like terms
Now, we'll perform the arithmetic operations on these like terms:
[tex]\[
16bc - 6bc = 10bc
\][/tex]
[tex]\[
-12cd + 8cd = -4cd
\][/tex]
The term [tex]\(4bd\)[/tex] remains as it is because there are no other [tex]\(bd\)[/tex] terms to combine with:
[tex]\[
4bd
\][/tex]
### Step 4: Write the simplified expression
Finally, we write down the simplified expression by combining all the simplified like terms:
[tex]\[
10bc - 4cd + 4bd
\][/tex]
So, the simplified expression for [tex]\((16bc - 12cd) + (8cd - 6bc + 4bd)\)[/tex] is:
[tex]\[
10bc - 4cd + 4bd
\][/tex]
