To rewrite the expression \((3x - 5)(2x + 2)\) using the Distributive Property, you need to distribute each term in the first parentheses by each term in the second parentheses.

Question

Here’s the step-by-step breakdown:

1. **Distribute \(3x\) to both terms in the second parentheses**:
\[
3x \cdot 2x = 6x^2
\]
\[
3x \cdot 2 = 6x
\]

2. **Distribute \(-5\) to both terms in the second parentheses**:
\[
-5 \cdot 2x = -10x
\]
\[
-5 \cdot 2 = -10
\]

3. **Now combine all the results together**:
\[
6x^2 + 6x - 10x - 10
\]

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

Thus, the expression \((3x - 5)(2x + 2)\) when rewritten using the Distributive Property is:
\[
6x^2 - 4x - 10
make this like a 7th grader wrote it

Answer 1

Sure! Here’s how a 7th grader might rewrite the expression \((3x - 5)(2x + 2)\) using the Distributive Property:

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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!