Sure, let's go through the addition of the two given polynomials step by step.
Given polynomials:
1. [tex]\( P_1 = 12bc - 16cd \)[/tex]
2. [tex]\( P_2 = 8cd - 6bc + 4bd \)[/tex]
We need to add [tex]\( P_1 \)[/tex] and [tex]\( P_2 \)[/tex]:
[tex]\[ P_1 + P_2 = (12bc - 16cd) + (8cd - 6bc + 4bd) \][/tex]
Let's rearrange and combine like terms:
[tex]\[ (12bc - 6bc) + (-16cd + 8cd) + 4bd \][/tex]
Now let's perform the addition step by step:
1. Combine the [tex]\( bc \)[/tex]-terms:
[tex]\[ 12bc - 6bc = 6bc \][/tex]
2. Combine the [tex]\( cd \)[/tex]-terms:
[tex]\[ -16cd + 8cd = -8cd \][/tex]
3. The term [tex]\( 4bd \)[/tex] does not have any like terms to combine with:
[tex]\[ 4bd \][/tex]
Putting it all together, we get:
[tex]\[ 6bc - 8cd + 4bd \][/tex]
So the result of adding the polynomials is:
[tex]\[ 6bc - 8cd + 4bd \][/tex]
This is the simplified form of the sum of the two given polynomials.
