To determine how much more it costs to make [tex]\( b \)[/tex] necklaces than [tex]\( b \)[/tex] bracelets, we need to compare the cost of making [tex]\( b \)[/tex] necklaces to the cost of making [tex]\( b \)[/tex] bracelets.
1. Cost of making [tex]\( b \)[/tex] bracelets:
The cost function for [tex]\( b \)[/tex] bracelets is given by:
[tex]\[
4 + 5b
\][/tex]
2. Cost of making [tex]\( b \)[/tex] necklaces:
The cost function for [tex]\( b \)[/tex] necklaces is given by:
[tex]\[
8b + 6
\][/tex]
3. Difference in cost between necklaces and bracelets:
To find how much more it costs to make [tex]\( b \)[/tex] necklaces than [tex]\( b \)[/tex] bracelets, we subtract the cost of making [tex]\( b \)[/tex] bracelets from the cost of making [tex]\( b \)[/tex] necklaces:
[tex]\[
(8b + 6) - (4 + 5b)
\][/tex]
4. Simplify the expression:
We simplify the resulting expression step-by-step:
[tex]\[
(8b + 6) - (4 + 5b) = 8b + 6 - 4 - 5b
\][/tex]
Combine like terms:
[tex]\[
8b - 5b + 6 - 4 = 3b + 2
\][/tex]
So, the polynomial that represents how much more it costs to make [tex]\( b \)[/tex] necklaces than [tex]\( b \)[/tex] bracelets is:
[tex]\[
3b + 2
\][/tex]
