## baby456 one year ago Please help me with factoring 10m^3n^2-15m^2n^1 medal + fan just don't just give me the answer. Explain IT.

1. baby456

@mathstudent55

2. baby456

@dajakesta

3. mathstudent55

$$\large 10m^3n^2-15m^2n^1$$ You are factoring a two-term polynomial. Start by factoring a common factor out of both terms. What is the GCF of both terms?

4. baby456

5

5. mathstudent55

Correct. For the number parts, 10 and -15, you can factor out 5. What about for the variable parts? What do m^3 and m^2 have in common?

6. baby456

6

7. mathstudent55

Not a number. It's a variable to a power.

8. mathstudent55

|dw:1435094377519:dw|

9. mathstudent55

m^3 and m^2 have m^2 in common.

10. mathstudent55

Then we see what n^2 and n^1 have in common. |dw:1435094442799:dw| n^2 and n^1 have n in common.

11. mathstudent55

That means the GCF of the two terms is 5m^2n

12. baby456

how did you get 2 from

13. mathstudent55

The common factor is $$\large 5m^2n$$ The 2 is the exponent of the m.

14. baby456

ok

15. mathstudent55

$$\large 10m^3n^2-15m^2n^1$$ Now we factor out the GCF: $$\large =5m^2n(~~~~~~~~~~~~~~)$$

16. baby456

how? i dont know i am so confused

17. baby456

what gcf

18. mathstudent55

$$\large =5m^2n(2mn - 3)$$

19. baby456

where are you getting the 2 and 3

20. mathstudent55

The 2 and the 3 are the numbers you need so that when you multiply by the 5 outside you get back the 10 and 15 you started with.

21. mathstudent55

Factoring is the opposite of the distributive property.

22. baby456

i dont get it

23. mathstudent55

Let me go back a few steps and show a simple example. Do you know the distributive property?

24. baby456

what?

25. mathstudent55

Use the distributive property to simplify this expression: $$2(3 + 5)$$

26. baby456

11 i think

27. mathstudent55

No. I'll show you. The distributive property of multiplication over addition is this: $$2(3 + 5) = 2 \times 3 + 2 \times 5$$

28. mathstudent55

|dw:1435095136526:dw|

29. mathstudent55

The distributive property shows you that you multiply the number outside parentheses by each of the numbers inside the parentheses. The you add the products.

30. mathstudent55

Here is another example: |dw:1435095244847:dw|

31. baby456

ok

32. baby456

but how does that help with factoring.

33. mathstudent55

Factoring is doing the distributive property in reverse.

34. mathstudent55

Here is an example of the distributive property using variables. |dw:1435095365764:dw|

35. baby456

ok

36. mathstudent55

We went from a product of a variable, m, and a binomial, 2m + n, to a result, $$2m^2 + mn$$

37. mathstudent55

Now let's do that problem in reverse. Let's say we are given the final answer above, and we are asked to factor.

38. mathstudent55

This is the problem we have now: |dw:1435095505073:dw|

39. mathstudent55

First, we find the greatest common factor of the two terms.

40. mathstudent55

|dw:1435095568553:dw|

41. mathstudent55

Now we take the problem, and we do the distributive property in reverse.

42. mathstudent55

We need to find what to place inside the parentheses to get back to our original problem. |dw:1435095632204:dw|

43. mathstudent55

|dw:1435095685363:dw|

44. mathstudent55

|dw:1435095737610:dw|

45. mathstudent55

|dw:1435095761968:dw|

46. mathstudent55

|dw:1435095800516:dw|

47. baby456

i dont get it. it like my brain is stuck.

48. mathstudent55

This is the answer: |dw:1435095820650:dw|