Question

Multiply the polynomials 2x - 2 * 3x + 5

Answer 1

To multiply the polynomials \( (2x - 2) \) and \( (3x + 5) \), we can use the distributive property (also known as the FOIL method for binomials).

Let's compute the product step-by-step:

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

1. Multiply \( 2x \) by \( 3x \):
\[
2x \cdot 3x = 6x^2
\]

2. Multiply \( 2x \) by \( 5 \):
\[
2x \cdot 5 = 10x
\]

3. Multiply \( -2 \) by \( 3x \):
\[
-2 \cdot 3x = -6x
\]

4. Multiply \( -2 \) by \( 5 \):
\[
-2 \cdot 5 = -10
\]

Now, we can combine all these results:

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

Now, combine the like terms \( 10x \) and \( -6x \):

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

So, the product of the polynomials \( (2x - 2) \) and \( (3x + 5) \) is:

\[
\boxed{6x^2 + 4x - 10}
\]