(2x−1)(2x 2 −9x+3)

Sure, let's solve this step by step:

First, let's write down the expression:

(2x−1)(2x^2 −9x+3)

This is a multiplication of a binomial (2x-1) and a trinomial (2x^2 - 9x + 3). We can use the distributive property (also known as the FOIL method) to multiply these together.

First, multiply the first terms in each binomial:

2x * 2x^2 = 4x^3

Next, multiply the outer terms:

2x * -9x = -18x^2

Then, multiply the inner terms:

-1 * 2x^2 = -2x^2

Finally, multiply the last terms:

-1 * 3 = -3

Now, add all these terms together:

4x^3 - 18x^2 - 2x^2 - 3

Combine like terms:

4x^3 - 20x^2 - 3

So, (2x−1)(2x^2 −9x+3) simplifies to 4x^3 - 20x^2 - 3.