Let's simplify each expression step by step.
Simplifying \( (3z + 5yz + 3y) - (2yz - 5z^2 - 17z) \):
First, distribute the negative sign across the second set of parentheses:
\[ (3z + 5yz + 3y) -2yz + 5z^2 + 17z \]
Now, combine like terms:
\[ 3z + 17z + 5z^2 + 5yz - 2yz + 3y \]
This simplifies to:
\[ (3z + 17z) + 5z^2 + (5yz - 2yz) + 3y = 20z + 5z^2 + 3y + 3yz \]
So, the final answer is: \[ 5z^2 + 20z + 3y + 3yz \]
Simplifying \( (10t^5 - 5t^{11}) (10t^3 + 2t^2) \):
Use the distributive property (FOIL method):
\[ = 10t^5 \cdot 10t^3 + 10t^5 \cdot 2t^2 - 5t^{11} \cdot 10t^3 - 5t^{11} \cdot 2t^2 \]
Calculating each term, we have:
- \( 10t^5 \cdot 10t^3 = 100t^{8} \)
- \( 10t^5 \cdot 2t^2 = 20t^{7} \)
- \( -5t^{11} \cdot 10t^3 = -50t^{14} \)
- \( -5t^{11} \cdot 2t^2 = -10t^{13} \)
Now, combining all these terms, we get:
\[ -50t^{14} - 10t^{13} + 20t^7 + 100t^8 \]
Therefore, the final result is:
\[ -50t^{14} - 10t^{13} + 100t^8 + 20t^7 \]
So, your final answers are:
- \( 5z^2 + 20z + 3y + 3yz \)
- \( -50t^{14} - 10t^{13} + 100t^8 + 20t^7 \)