Simplify each fraction COMPLETELY. (HINT: list the GCF of each number first) 3) 12184) 1545

  1

Step-by-step explanation:

Gcf of 3 : 1  *  3

Gcf of 12184 : 1 *  12184

                       2  * 6092

                       4 * 3046

                         8 * 1523

Gcf of  1545:     1  * 1545

                          3  * 515

                            5  * 309

All the the numbers do not have any common number except 1 so therefore 1 is the only common number which makes It the GCF in all three numbers.

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