Question
Ise the distributive property to write an equivalent expression.
Ask by Lambert Bernard. in the United States
Jan 24,2025
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Tutor-Verified Answer
Answer
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.
Solution
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!
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Let’s break down the distributive property! If you have an expression like \( a(b + c) \), you can distribute the \( a \) to both terms in the parentheses. This means you’ll do \( a \cdot b + a \cdot c \). So, if we say \( 3(x + 4) \), using the distributive property gives you \( 3x + 12 \). A common mistake is forgetting to distribute to both terms! For example, if someone mistakenly writes just \( 3x + 4 \) instead of \( 3x + 12 \), they’re losing part of that equation. Always remember, every term in the parentheses gets a dose of the distributive property!
