Question

Find the product of the polynomials (9x2−6x+1)(3x−1) .(1 point) Responses 27x3+27x2+9x+1 27 x cubed plus 27 x squared plus 9 x plus 1 27x3−27x2+9x−1 27 x cubed minus 27 x squared plus 9 x minus 1 27x3−27x4+9x−1 27 x cubed minus 27 x superscript 4 baseline plus 9 x minus 1 27x3−9x2+27x−1

Answer 1

To find the product of the polynomials \( (9x^2 - 6x + 1)(3x - 1) \), we can use the distributive property (also known as the distributive law of multiplication over addition).

Let's distribute \( (3x - 1) \) to each term in \( (9x^2 - 6x + 1) \):

1. Distributing \( 3x \):
\[
3x \cdot 9x^2 = 27x^3
\]
\[
3x \cdot (-6x) = -18x^2
\]
\[
3x \cdot 1 = 3x
\]

2. Distributing \( -1 \):
\[
-1 \cdot 9x^2 = -9x^2
\]
\[
-1 \cdot (-6x) = 6x
\]
\[
-1 \cdot 1 = -1
\]

Now, we can combine all these terms together:
\[
27x^3 + (-18x^2 - 9x^2) + (3x + 6x) - 1
\]
This simplifies to:
\[
27x^3 - 27x^2 + 9x - 1
\]

The final product of the polynomials \( (9x^2 - 6x + 1)(3x - 1) \) is:
\[
27x^3 - 27x^2 + 9x - 1
\]

Therefore, the correct response is:
\[
27x^3 - 27x^2 + 9x - 1
\]