The document shows a student's work solving a math problem to find the total mass of three boxes of sweets where the masses are given as functions of c and d. The student derived the total mass as (16c-6d)g, but the book answer was (16c-6d)g, then 2(8c-3d)g. The solution shows collecting like terms of c and d with their signs to get (16c-6d)g as the total, which is then factored as 2(8c-3d)g since 2 is a common multiplier in the brackets.

1. the answer i derived is (16c-6d)g. but the answer shown in my book is (16c-6d)g, then 2(8c-3d)g.
why so? this is the question: the masses of 3 boxes of sweets are (-c-4d)g, (6c-3d)g, and
(11c+d)g. find the total mass.
Solution
The total mass of three boxes of sweets = (-c-4d)g+ (6c-3d)g, +(11c+d)g.
= (-c+6c+11c)g+(-4d-3d+d)d, collecting c's together and d's together along with their signs.
=(16c-6d)g is the total mass of sweets.
=(2*8c-2*3d)g, 2 is common multiplier insidethe bracket which could be taken out.
=2(8c-3d)g