Question

what is ((x^2 - 3x + 1)(7x^2 - 7x - 6))?
a. (7x^4 - 28x^3 + 22x^2 + 11x - 6)
b. (7x^4 - 28x^3 + 22x^2 + 12x - 6)
c. (7x^4 - 28x^3 + 21x^2 + 11x - 5)
d. (7x^4 - 29x^3 + 21x^2 + 11x - 6)

Explanation:

Step1: Distribute each term

$x^2(7x^2-7x-6) -3x(7x^2-7x-6) +1(7x^2-7x-6)$

Step2: Expand each product

$7x^4-7x^3-6x^2 -21x^3+21x^2+18x +7x^2-7x-6$

Step3: Combine like terms

$7x^4 + (-7x^3-21x^3) + (-6x^2+21x^2+7x^2) + (18x-7x) -6$

Step4: Simplify the expression

$7x^4 -28x^3 +22x^2 +11x -6$

Answer:

a. $7x^4 - 28x^3 + 22x^2 + 11x - 6$