Sure, let's analyze and simplify the given expression step-by-step.
### Expression Analysis:
The expression provided is:
[tex]\[ 5 p^2 + 12 q^2 \][/tex]
This expression contains two separate terms:
- The first term is [tex]\( 5 p^2 \)[/tex]
- The second term is [tex]\( 12 q^2 \)[/tex]
### Breakdown of Each Term:
1. For the term [tex]\( 5 p^2 \)[/tex]
- The coefficient is [tex]\( 5 \)[/tex].
- The variable is [tex]\( p \)[/tex].
- The exponent of the variable [tex]\( p \)[/tex] is [tex]\( 2 \)[/tex], indicating it is squared.
2. For the term [tex]\( 12 q^2 \)[/tex]
- The coefficient is [tex]\( 12 \)[/tex].
- The variable is [tex]\( q \)[/tex].
- The exponent of the variable [tex]\( q \)[/tex] is [tex]\( 2 \)[/tex], indicating it is squared.
### Combining the Terms:
The expression [tex]\( 5 p^2 + 12 q^2 \)[/tex] is already in its simplest form as it is a sum of terms where each term involves different variables raised to a power and multiplied by a constant coefficient.
### Conclusion:
The final expression, therefore, remains:
[tex]\[ 5 p^2 + 12 q^2 \][/tex]
This is the simplified form of the given polynomial expression.
