Answer :
Sure, let's solve the problem:
We need to find the product of [tex]\((3x^2 - 5x + 3)(3x - 2)\)[/tex].
To do this, we will use the distributive property (also known as the FOIL method for binomials, though this applies here for more complex polynomials).
### Steps to Solve
1. Multiply each term in the first polynomial by each term in the second polynomial.
2. Combine like terms.
Let's go through this step-by-step:
1. Distribute (3x - 2) to each term in [tex]\(3x^2 - 5x + 3\)[/tex]:
- Distribute [tex]\(3x\)[/tex]:
[tex]\[
3x \cdot 3x^2 = 9x^3
\][/tex]
[tex]\[
3x \cdot -5x = -15x^2
\][/tex]
[tex]\[
3x \cdot 3 = 9x
\][/tex]
- Distribute [tex]\(-2\)[/tex]:
[tex]\[
-2 \cdot 3x^2 = -6x^2
\][/tex]
[tex]\[
-2 \cdot -5x = 10x
\][/tex]
[tex]\[
-2 \cdot 3 = -6
\][/tex]
2. Combine all these products:
[tex]\[
9x^3 - 15x^2 + 9x - 6x^2 + 10x - 6
\][/tex]
3. Combine like terms:
[tex]\[
9x^3 + (-15x^2 - 6x^2) + (9x + 10x) - 6
\][/tex]
Simplify:
[tex]\[
9x^3 - 21x^2 + 19x - 6
\][/tex]
So, the product of [tex]\(\left(3x^2 - 5x + 3\right)(3x - 2)\)[/tex] is:
[tex]\[
9x^3 - 21x^2 + 19x - 6
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{9x^3 - 21x^2 + 19x - 6}
\][/tex]
We need to find the product of [tex]\((3x^2 - 5x + 3)(3x - 2)\)[/tex].
To do this, we will use the distributive property (also known as the FOIL method for binomials, though this applies here for more complex polynomials).
### Steps to Solve
1. Multiply each term in the first polynomial by each term in the second polynomial.
2. Combine like terms.
Let's go through this step-by-step:
1. Distribute (3x - 2) to each term in [tex]\(3x^2 - 5x + 3\)[/tex]:
- Distribute [tex]\(3x\)[/tex]:
[tex]\[
3x \cdot 3x^2 = 9x^3
\][/tex]
[tex]\[
3x \cdot -5x = -15x^2
\][/tex]
[tex]\[
3x \cdot 3 = 9x
\][/tex]
- Distribute [tex]\(-2\)[/tex]:
[tex]\[
-2 \cdot 3x^2 = -6x^2
\][/tex]
[tex]\[
-2 \cdot -5x = 10x
\][/tex]
[tex]\[
-2 \cdot 3 = -6
\][/tex]
2. Combine all these products:
[tex]\[
9x^3 - 15x^2 + 9x - 6x^2 + 10x - 6
\][/tex]
3. Combine like terms:
[tex]\[
9x^3 + (-15x^2 - 6x^2) + (9x + 10x) - 6
\][/tex]
Simplify:
[tex]\[
9x^3 - 21x^2 + 19x - 6
\][/tex]
So, the product of [tex]\(\left(3x^2 - 5x + 3\right)(3x - 2)\)[/tex] is:
[tex]\[
9x^3 - 21x^2 + 19x - 6
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{9x^3 - 21x^2 + 19x - 6}
\][/tex]
