Alright, let's simplify the given expression step by step:
The expression to simplify is:
[tex]\[ 3m^2 + 12m^2 - 36m^4n^3 - 48m^5n^2 \][/tex]
Step 1: Combine Like Terms
First, we combine the like terms:
[tex]\[ (3m^2 + 12m^2) - 36m^4n^3 - 48m^5n^2 \][/tex]
[tex]\[ 15m^2 - 36m^4n^3 - 48m^5n^2 \][/tex]
Step 2: Factor Out Common Terms
Now, we look for any common factors in the terms.
Notice that we can factor [tex]\( m^2 \)[/tex] out from every term:
[tex]\[ m^2(15 - 36m^2n^3 - 48m^3n^2) \][/tex]
Step 3: Renaming for Simplification (Optional)
Since there are no common factors among terms inside the parentheses, we rewrite the expression:
[tex]\[ m^2(15 - 36m^2n^3 - 48m^3n^2) \][/tex]
Thus, the simplified expression is:
[tex]\[ m^2(-48m^3n^2 - 36m^2n^3 + 15) \][/tex]
So, the fully simplified form of the given expression is:
[tex]\[ m^2(-48m^3n^2 - 36m^2n^3 + 15) \][/tex]
