TIME REMAINING 59:13 The fine schedule for overdue books at the county library is modeled by the values in the table. Library Fines for Overdue Books Days overdue Amount of fine 0 0 ¢ 2 5 ¢ 4 10 ¢ 6 15 ¢ 8 20 ¢ 10 25 ¢ Which equation best models the fine schedule for overdue books? , where x is the cost in cents for a book that is y days overdue , where y is the cost in cents for a book that is x days overdue , where x is the cost in cents for a book that is y days overdue , where y is the cost in cents for a book that is x days overdue

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answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)