## morganalana17 2 years ago green

1. blurbendy

I know about Pascal's triangle, but I don't know if that's what you're referring to.

2. blurbendy

Sure, do need an explanation of what it is, or do you have a problem you want me to look at?

3. blurbendy

you*

4. hba
5. blurbendy

Sure, do you know how to expand a binomial (something)^2?

6. blurbendy

Okay, let's start there then. Say you have something like (x + y)^2 and we want to expand that. You can rewrite (x + y)^2 so that it's like: (x + y)(x + y) Make sense so far?

7. blurbendy

Good, now we're going to multiply the first x in (x + y) to BOTH the (x + y) in the other term to get: x^2 + xy |dw:1358369073609:dw|

8. blurbendy

Make sense?

9. precal

pascal's triangle is use to expand

10. precal

|dw:1358369183479:dw|

11. blurbendy

Great, then we move on and do the same thing with the first y. and get xy + y^2, so in total we have x^2 + xy + xy + y^2

12. precal

|dw:1358369198853:dw|do you see the pattern?

13. blurbendy

@precal, that's what im attempting to show. thanks for the visual though :)

14. blurbendy

perfect, so we have x^2 + xy + xy + y^2 which equals x^2 + 2xy + y^2, which is what precal's picture shows

15. precal

|dw:1358369366989:dw|

16. precal

|dw:1358369387693:dw|then notice what is happening to the x powers and then the y powers

17. precal

x powers start at 2 while y start at 0

18. precal

this is the pattern you will follow for you problem

19. blurbendy

Now, if we wanted to take that further like (x +y)^3 (like your problem) we can do two things.

20. precal

|dw:1358369548166:dw|you will use the 3rd row

21. precal

|dw:1358369588020:dw|

22. blurbendy

We could multiply (x + y)(x^2 + 2xy + y^2) And do the EXACT same thing like how we were multiplying the x to the second term and then the y to the second term.

23. blurbendy

That would give us the correct answer, OR we could use the pattern precal is showing us.

24. precal

|dw:1358369600649:dw|

25. precal

be careful with your second term because of the negative, just simplify and you are done

26. precal

yw