You are asked to draw a triangle with side lengths of 8 inches and 10 inches. What is the longest whole number length that your third side can be? Hint: set up 4 triangles with measures below to test which will make a triangle:

8in,10in,17in

8in, 10in, 18in

8in, 10in, 20in

8in,10in,21in

b and c

step-by-step explanation:

i believe it's a.

i'm not sure on this one, most likely correct.

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)