Ise the distributive property to write an equivalent expression.

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UpStudy AI · Accepted Answer

Certainly! The **distributive property** allows you to multiply a single term by each term inside a set of parentheses. It helps in expanding expressions and simplifying calculations.

### **Distributive Property Formula:**
$$ a(b + c) = ab + ac $$
$$ a(b - c) = ab - ac $$

### **Example 1:**

**Expression:**  
$$ 5(x + 3) $$

**Applying Distributive Property:**  
$$ 5 \cdot x + 5 \cdot 3 = 5x + 15 $$

**Equivalent Expression:**  
$$ 5x + 15 $$

### **Example 2:**

**Expression:**  
$$ 2(4y - 7) $$

**Applying Distributive Property:**  
$$ 2 \cdot 4y - 2 \cdot 7 = 8y - 14 $$

**Equivalent Expression:**  
$$ 8y - 14 $$

### **Example 3:**

**Expression:**  
$$ -3(2a + 5b - c) $$

**Applying Distributive Property:**  
$$ -3 \cdot 2a + (-3) \cdot 5b + (-3) \cdot (-c) = -6a - 15b + 3c $$

**Equivalent Expression:**  
$$ -6a - 15b + 3c $$

### **Steps to Apply the Distributive Property:**

1. **Multiply** the term outside the parentheses by **each** term inside the parentheses.
2. **Change** the sign as necessary based on the operation (addition or subtraction).
3. **Simplify** the resulting expression by combining like terms if possible.

If you have a specific expression you'd like to simplify using the distributive property, feel free to share it!
Use the distributive property to multiply the term outside the parentheses by each term inside, then simplify the expression by combining like terms if possible.

Ise the distributive property to write an equivalent expression.

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