Question

.Using the Distributive Property to rewrite the expression (3x – 5)(2x + 2)

Answer 1

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.

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:
\[
6x^2 - 4x - 10
\]