Question

Find the product of the polynomials (9x^2−6x+1)(3x−1)
.

Answer 1

To find the product of the two polynomials, we need to multiply every term in the first polynomial by every term in the second polynomial.

First, distribute the first term of the first polynomial (9x^2) to both terms in the second polynomial (3x and -1):

9x^2 * 3x = 27x^3
9x^2 * -1 = -9x^2

Next, distribute the second term of the first polynomial (-6x) to both terms in the second polynomial (3x and -1):

-6x * 3x = -18x^2
-6x * -1 = 6x

Finally, distribute the third term of the first polynomial (1) to both terms in the second polynomial (3x and -1):

1 * 3x = 3x
1 * -1 = -1

Now, combine all the terms:

(27x^3) + (-9x^2) + (-18x^2) + (6x) + (3x) + (-1)
= 27x^3 - 27x^2 + 9x - 1

Therefore, the product of the polynomials (9x^2−6x+1)(3x−1) is 27x^3 - 27x^2 + 9x - 1.