1. robert made the following rectangles using algebra tiles and wrote the expression 2(x + x - 12)
(representing both rectangles)
-1 -1 - -
- - - -
-1-1-1-1
-
-
x
-1 - -1 -
-1 -1 -
11
-1 -1 -1 -1
a. how can he write the expression as a fully factored product?
b. how can he write the expression as a sum?

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)

the answer is b

step-by-step explanation: