Write two equivalent expressions by factoring out two different greatest common factors.

6x-18y+36

The two equivalent expressions by factoring out two different greatest common factors are 6 (x - 3y + 6) and 3 (2x - 6y + 12)

Solution:

Given that, we have to write two equivalent expressions by factoring out two different greatest common factors

Given expression is:

6x - 18y + 36

First find the factors of 6, 18 and 36

The factors of 6 are: 1, 2, 3, 6

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

Then the greatest common factor is 6

Factor out 6 from given expression

6x - 18y + 36 = 6 (x - 3y + 6)

Thus one of equivalent expression is 6 (x - 3y + 6)

Second greatest common factor is 3

Factor out 3 from given expression

6x - 18y + 36 = 3 (2x - 6y + 12)

Thus another equivalent expression is 3 (2x - 6y + 12)