To solve the expressions using the distributive property, we will distribute the terms inside the parentheses and then combine like terms.
1. For the expression \( 5(3y - 2) - (7y + 2) \):
Step 1: Distribute \( 5 \) in the first term: \[ 5(3y) - 5(2) = 15y - 10 \]
Step 2: Distribute the negative sign in the second term: \[ -(7y + 2) = -7y - 2 \]
Step 3: Combine the results: \[ 15y - 10 - 7y - 2 \]
Step 4: Combine like terms: \[ (15y - 7y) + (-10 - 2) = 8y - 12 \]
So, the final result for the first expression is: \[ \boxed{8y - 12} \]
2. For the expression \( 4(5y - 3) - (6y + 3) \):
Step 1: Distribute \( 4 \) in the first term: \[ 4(5y) - 4(3) = 20y - 12 \]
Step 2: Distribute the negative sign in the second term: \[ -(6y + 3) = -6y - 3 \]
Step 3: Combine the results: \[ 20y - 12 - 6y - 3 \]
Step 4: Combine like terms: \[ (20y - 6y) + (-12 - 3) = 14y - 15 \]
So, the final result for the second expression is: \[ \boxed{14y - 15} \]