Mr Ludwig wrote the following question as a bonus on this week's quiz "My car can hold 12 65 galons of gas. I drive 24.9 miles for every gallon of gas used. How many miles can I drive on a full tank?
Some of the student responses are shown in the table below
Student
Response
Liam
12.65
+ 24.90
37.55
Noelle
24.90
12.65
1225
Madeleine
12.65
24.9
31.4985
12.65
24.9
Yesinia
314.985
Which students answered incorrectly? Why are they wrong?
B
IŲ 2

so then what are you asking?

step-by-step explanation:

hello from mrbilldoesmath!

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)