Step 1a

The given polynomial \$(2x^2 − 3x + 1)\$ and (3x + 2)

Let’s start multiplying:

\$2x^2\$ multiplied by 3x: \$2x^2 times 3x\$ = \$6x^3\$
\$2x^2\$ multiplied by 2: \$2x^2 times 2\$ = \$4x^2\$
− 3x multiplied by 3x: \$-3x times 3x \$ = \$ - 9x^2\$
- 3x multiplied by 2: \$-3x times 2\$ = - 6x
1 multiplied by 3x: \$1 times 3x\$ = 3x
1 multiplied by 2: \$ 2 times 1\$ = 2

Explanation: This involves multiplying every term in the polynomial by each term in the polynomial expression to expand it fully.

Step 1b

Now, let’s add up all the results:
\$6x^3 + 4x^2 - 9x^2 - 6x +3x +2\$
Combining like terms:
\$6x^3 − 5x^2 − 3x + 2\$
So, the product of \$(2x^2 − 3x + 1)\$ and (3x+2) is \$6x^3 − 5x^2 − 3x + 2\$.

Explanation: Multiply each term, sum the products, and then consolidate terms for the final result.