Question

To simplify \((3x - 5)(2x + 2)\), we can use the Distributive Property where we multiply each term in the first part by each term in the second part. Here’s how we do it step by step:

1. **First, we take \(3x\) and multiply it by both terms in the second parentheses**:
- First, \(3x \cdot 2x = 6x^2\) (this is like multiplying the numbers and adding the exponents)
- Then, \(3x \cdot 2 = 6x\) (just multiply the numbers)

2. **Next, we take \(-5\) and multiply it by both terms in the second parentheses**:
- First, \(-5 \cdot 2x = -10x\) (negative five times positive two gives negative ten)
- Then, \(-5 \cdot 2 = -10\) (negative five times positive two gives negative ten again)

3. **Now, we combine everything we got together**:
\[
6x^2 + 6x - 10x - 10
\]

4. **Finally, we need to combine like terms** (the \(6x\) and \(-10x\)):
- So, \(6x - 10x = -4x\)

Putting it all together, we get:
\[
6x^2 - 4x - 10
\]

So, the simplified version of \((3x - 5)(2x + 2)\) is:
\[
6x^2 - 4x - 10
\]

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And that’s how you use the Distributive Property to simplify that expression!
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Answer 1

To simplify \((3x - 5)(2x + 2)\) using the Distributive Property, we proceed as follows:

1. **Distribute \(3x\)**:
- \(3x \cdot 2x = 6x^2\)
- \(3x \cdot 2 = 6x\)

2. **Distribute \(-5\)**:
- \(-5 \cdot 2x = -10x\)
- \(-5 \cdot 2 = -10\)

3. **Combine the results**:
\[
6x^2 + 6x - 10x - 10
\]

4. **Combine like terms**:
\[
6x^2 - 4x - 10
\]

Thus, the simplified version of \((3x - 5)(2x + 2)\) is:
\[
6x^2 - 4x - 10
\]