Expand and fully simplify the following expression: $$ 3(r-1)+2(3 r+5) $$

Question

UpStudy AI · Accepted Answer

To expand and fully simplify the expression:

$$
3(r - 1) + 2(3r + 5)
$$

follow these steps:

### **Step 1: Apply the Distributive Property**

The distributive property states that $$ a(b + c) = ab + ac $$. We'll apply this property to both terms in the expression.

1. **First Term: $$ 3(r - 1) $$**
   $$
   3 \times r = 3r
   $$
   $$
   3 \times (-1) = -3
   $$
   So,
   $$
   3(r - 1) = 3r - 3
   $$

2. **Second Term: $$ 2(3r + 5) $$**
   $$
   2 \times 3r = 6r
   $$
   $$
   2 \times 5 = 10
   $$
   So,
   $$
   2(3r + 5) = 6r + 10
   $$

### **Step 2: Combine the Expanded Terms**

Now, combine the results from both terms:

$$
3r - 3 + 6r + 10
$$

### **Step 3: Combine Like Terms**

Combine the terms that have the same variable and the constant terms separately:

1. **Combine the $$ r $$-terms:**
   $$
   3r + 6r = 9r
   $$

2. **Combine the constant terms:**
   $$
   -3 + 10 = 7
   $$

### **Final Simplified Expression**

Putting it all together:

$$
9r + 7
$$

**Therefore, the fully simplified expression is:**

$$
9r + 7
$$
The simplified expression is $$ 9r + 7 $$.

Expand and fully simplify the following expression: