The two equivalent expressions by factoring out two different greatest common factors are 6(x - 3y + 6) and 3(2x - 6y + 12)
<em><u>Solution:</u></em>
Given that, we have to write two equivalent expressions by factoring out two different greatest common factors
Given expression is:
6x - 18y + 36
<em><u>First find the factors of 6, 18 and 36</u></em>
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
<em><u>Factor out 6 from given expression</u></em>
6x - 18y + 36 = 6(x - 3y + 6)
Thus one of equivalent expression is 6(x - 3y + 6)
Second greatest common factor is 3
<em><u>Factor out 3 from given expression</u></em>
6x - 18y + 36 = 3(2x - 6y + 12)
Thus another equivalent expression is 3(2x - 6y + 12)
