Use the Distributive Property to rewrite the expression (3x−5)(2x+2)

Question

.(1 point)
Responses

6x2−4x−10
6 x squared minus 4 x minus 10

x2−3x−10
x squared minus 3 x minus 10

5x2−2x−3
5 x squared minus 2 x minus 3

6x2−3x−10

Answer 1

To use the Distributive Property, we will distribute each term in the first expression to each term in the second expression:

\((3x - 5)(2x + 2)\)

We will use the distributive property as follows:

1. Distribute \(3x\) to both terms in \((2x + 2)\):

   \[ 3x \cdot 2x = 6x^2 \] \[ 3x \cdot 2 = 6x \]

2. Distribute \(-5\) to both terms in \((2x + 2)\):

   \[ -5 \cdot 2x = -10x \] \[ -5 \cdot 2 = -10 \]

Now we can combine all the results:

\[ 6x^2 + 6x - 10x - 10 \]

Now combine like terms:

\[ 6x^2 + (6x - 10x) - 10 = 6x^2 - 4x - 10 \]

Thus, the expression rewritten using the Distributive Property is:

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

So the correct response is:

6x² - 4x - 10