What is the product of (a - 1) and (2a + 2)?

To find the product of the expressions (a - 1) and (2a + 2), you can apply the distributive property. This involves multiplying each term in the first expression by each term in the second expression.

First, distribute (a - 1) over (2a + 2):

1. Multiply (a) by (2a):

   • This results in 2a^2.

2. Multiply (a) by (2):

   • This gives you 2a.

3. Multiply (-1) by (2a):

   • This results in -2a.

4. Multiply (-1) by (2):

   • This gives you -2.

Now, combine these results: 2a^2 + 2a - 2a - 2.

The terms 2a and -2a cancel each other out, leaving you with: 2a^2 - 2.

Next, you can factor out the common factor 2: 2(a^2 - 1).

The expression ( a^2 - 1 ) can be recognized as a difference of squares which can also be expressed as ( (a - 1)(a + 1) ), hence