Certainly! Let's solve the expression step by step.
We need to simplify and combine the two expressions:
[tex]\[ \left(2p^3 - 5pq^2 + 7pq\right) + \left(11p^2q - 4pq - 3\right) \][/tex]
First, let's rewrite the expression for clarity:
[tex]\[ 2p^3 - 5pq^2 + 7pq + 11p^2q - 4pq - 3 \][/tex]
Next, let's combine like terms. We will group the terms with the same powers of [tex]\( p \)[/tex] and [tex]\( q \)[/tex].
1. Combine terms with [tex]\( p^3 \)[/tex]:
[tex]\[ 2p^3 \][/tex]
2. Combine terms with [tex]\( p^2q \)[/tex]:
[tex]\[ 11p^2q \][/tex]
3. Combine terms with [tex]\( pq^2 \)[/tex]:
[tex]\[ -5pq^2 \][/tex]
4. Combine terms with [tex]\( pq \)[/tex]:
[tex]\[ 7pq - 4pq = 3pq \][/tex]
5. Constant term:
[tex]\[ -3 \][/tex]
Now, putting it all together, we get:
[tex]\[ 2p^3 + 11p^2q - 5pq^2 + 3pq - 3 \][/tex]
So, the simplified expression is:
[tex]\[ 2p^3 + 11p^2q - 5pq^2 + 3pq - 3 \][/tex]
This is the final result after combining like terms from the original expression.
