Question

1. what is $(x^{2}-3x + 1)(7x^{2}-7x - 6)$?

a. $7x^{4}-28x^{3}+21x^{2}+11x - 5$
b. $7x^{4}-28x^{3}+22x^{2}+11x - 6$
c. $7x^{4}-28x^{3}+22x^{2}+12x - 6$
d. $7x^{4}-29x^{3}+21x^{2}+11x - 6$

Explanation:

Step1: Distribute first term

$x^2(7x^2 -7x -6) = 7x^4 -7x^3 -6x^2$

Step2: Distribute second term

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

Step3: Distribute third term

$1(7x^2 -7x -6) = 7x^2 -7x -6$

Step4: Combine all terms

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

Step5: Combine like terms

$7x^4 + (-7x^3-21x^3) + (-6x^2+21x^2+7x^2) + (18x-7x) -6$
$=7x^4 -28x^3 +22x^2 +11x -6$

Answer:

b. $7x^{4}-28x^{3}+22x^{2}+11x-6$