Question

The distributive property.
1. 5(3y -2) -(7y + 2)
2. 4(5y -3) - (6y +3)

Answer 1

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:
\[
\boxed{14y - 15}
\]