Question

use the distributive property to rewrite the expression (2x - 2)(x - 6).
a 3x^2 - 10x - 8
b 2x^2 + 10x - 10
c 2x^2 - 14x + 12
d x^2 - 8x + 12

Answer 1

To use the distributive property to rewrite the expression \((2x - 2)(x - 6)\), we will apply the FOIL method (First, Outer, Inner, Last), which is a specific case of the distributive property for multiplying two binomials.

Let's calculate:

1. **First:** \(2x \cdot x = 2x^2\)
2. **Outer:** \(2x \cdot (-6) = -12x\)
3. **Inner:** \(-2 \cdot x = -2x\)
4. **Last:** \(-2 \cdot (-6) = 12\)

Now we add these results together:

\[
2x^2 - 12x - 2x + 12
\]

Combining like terms:

\[
2x^2 - 14x + 12
\]

So the expression \((2x - 2)(x - 6)\) simplifies to \(2x^2 - 14x + 12\).

Therefore, the correct answer is:

**c) \(2x^2 - 14x + 12\)**.