Rewrite each expression using the Distributive Property. $$ \begin{array}{ll} ext { 1. } \frac{32+4 x}{4} & ext { 2. } 15 x-10\end{array} $$

Question

Rewrite each expression using the Distributive Property. $$ \begin{array}{ll}	ext { 1. } \frac{32+4 x}{4} & 	ext { 2. } 15 x-10\end{array} $$

UpStudy AI · Accepted Answer

Sure! Let's apply the **Distributive Property** to each expression.

The **Distributive Property** states that for any real numbers $$ a $$, $$ b $$, and $$ c $$:

$$
a(b + c) = ab + ac
$$

This property also works in reverse, allowing you to factor out a common factor from terms.

### 1. $$ \frac{32 + 4x}{4} $$

**Step 1:** Distribute the division over each term in the numerator.

$$
\frac{32 + 4x}{4} = \frac{32}{4} + \frac{4x}{4}
$$

**Step 2:** Simplify each term.

$$
\frac{32}{4} = 8 \quad \text{and} \quad \frac{4x}{4} = x
$$

**Final Expression:**

$$
8 + x
$$

**Alternatively, factoring out the common factor 4:**

$$
\frac{32 + 4x}{4} = \frac{4(8 + x)}{4} = 8 + x
$$

### 2. $$ 15x - 10 $$

**Step 1:** Identify the greatest common factor (GCF) of the terms. Here, the GCF is **5**.

**Step 2:** Factor out the GCF using the reverse Distributive Property.

$$
15x - 10 = 5(3x) - 5(2)
$$

$$
= 5(3x - 2)
$$

**Final Expression:**

$$
5(3x - 2)
$$

---

**Summary of Rewritten Expressions:**

1. $$ \frac{32 + 4x}{4} = 8 + x $$

2. $$ 15x - 10 = 5(3x - 2) $$
1. $$ \frac{32 + 4x}{4} = 8 + x $$ 2. $$ 15x - 10 = 5(3x - 2) $$

Rewrite each expression using the Distributive Property. \( \begin{array}{ll}\text { 1. } \frac{32+4 x}{4} & \text { 2. } 15 x-10\end{array} \)