a. (x + 1)(1 + x - 2x + 3x - 4x) - (x - 1)(1 + x + 2x + 3x + 4x)
= (x + 1)(1 - 2x) - (x - 1)( 1 + 10x)
= x - 2x2 + 1 - 2x - x - 10x2 + 1 + 10x
= x - 2x - x + 10x - 2x2 - 10x2 + 1 + 1
= 8x - 8x2 + 2
= -8x + 8x + 2
= -(-8x + 8x + 2)
= 8x2 - 8x - 2
= 8x2 - 4x - 4x - 2
= 4x(2x - 1) - 2(2x + 1)
b. (2b2 - 2 - 5b + 6b3)(3 + 3b2 - b)
= (4b - 2 - 5b + 18b)(3 + 6b - b)
= (17b - 2)(3 + 5b)
= 51b + 85b2 - 6 + 10b
= 85b2 + 51b + 10b - 6
= \(51b\left(\dfrac{5}{3}+1\right)+6\left(\dfrac{5}{3}-1\right)\)
(2b2 - 2 - 5b + 6b3)(3 + 3b2 - b)
= 6b2 + 6b5 - 2b3 - 6 - 6b2 + 2b - 15b - 15b3 + 5b2 + 18b3 + 18b5 - 6b4
= 6b5 + 18b5 - 6b4 - 15b3 - 2b3 + 18b3 + 6b2 - 6b2 + 2b - 6
= 24b5 - 6b4 - 31b3 + 2b - 6