Student Activity Sheet 1; Overview 1. REVIEW Look at the patterns below. Can you find the next two items in each list and state the rule for finding them?
a. 2, 4, 6, 8, ...
b. 2, 3, 5, 9, 17, ...
c. 1, -2, 3, 4, 5, ...
d. 1, 4, 9, 16, ...

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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)

5.7622

step-by-step explanation:

the ten thousandths place is the 2. you round it up if, that number in whatever place is 5 or higher.