if each dimension of a unit cube is increased by 1. what is the ratio between the surface area of the new cube to that of the original

4:1 or 4/1

Step-by-step explanation:

Original surface area: Each side is 1 * 1 = 1 and there are 6 sides, so 1 * 6 = 6.

New surface area: Each side is 2*2 = 4, and there are 6 sides, so 4 * 6 = 24

The ratio would be 24:6, or 4:1. As a fraction, this would be 4/1

mxb67

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)