A bag is 14 inches tall, 10 inches wide, and 4 inches deep. Is it large enough to hold Natalie's school books, which have a combined volume of 500 cubic Inches? If so, much space will she have left? If not , how much more space will she need?

It is large enough to hold Natalie's books.

60 in^3 of space are left.

Step-by-step explanation:

The volume of the bag = 14 * 10 * 4 =  560  in^3.

So it is large enough hold Natalie's books with 560 - 500 = 60 in^3 left.

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step-by-step explanation:

hello from mrbilldoesmath!

answer:

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

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

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

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb