Find the product (1 - 3x) (x^2 - 6x - 4)x^2
A. -3x^5 + 19x^4 + 6x^3 - 4x^2
B. -3x^5 - 19x^4 + 6x^3 - 4x^2
C. -3x^5 + 19x^4 - 6x^3 - 4x^2
D.-3x^5 - 19x^4 - 6x^3 - 4x^2
Hmm. All the choices appear possible. I guess there's nothing for it but to go through the expansion. I get (A).
To find the product, we need to follow the distributive property and multiply each term of the first expression by each term of the second expression, and then by the third expression.
First, let's distribute the first expression (1 - 3x) to the second expression (x^2 - 6x - 4):
(1 - 3x)(x^2 - 6x - 4) = 1(x^2 - 6x - 4) - 3x(x^2 - 6x - 4)
= x^2 - 6x - 4 - 3x(x^2) + 3x(6x) + 3x(4)
Next, let's multiply the result from the previous step by the third expression (x^2):
(x^2 - 6x - 4 - 3x(x^2) + 3x(6x) + 3x(4)) * x^2 = x^2(x^2 - 6x - 4) - 3x(x^2)(x^2) + 3x(6x)(x^2) + 3x(4)(x^2)
= x^4 - 6x^3 - 4x^2 - 3x^5 + 18x^4 + 12x^3
Finally, let's rearrange the terms and combine like terms:
x^4 - 6x^3 - 4x^2 - 3x^5 + 18x^4 + 12x^3 = -3x^5 + 19x^4 + 6x^3 - 4x^2
So, the correct answer is (A) -3x^5 + 19x^4 + 6x^3 - 4x^2.