## anonymous one year ago will fan and medal~ polynomials and identities ~ Basically I have an assignment where I need to make my own polynomial identity

1. anonymous

Create your own using the columns below. See what happens when different binomials or trinomials are combined. Square one factor from column A and add it to one factor from column B to develop your own identity. Column A: (x − y) (x + y) (y + x) (y - x) Column B: (x2 + 2xy + y2) (x2 − 2xy + y2) (ax + b) (cy + d)

2. anonymous

So do what they say. Square one factor from column A and add it to one factor from column B to develop your own identity. Column A: $$(x + y)^2$$ Column B: $$(x^2 + 2xy + y^2)$$ add them $$(x + y)^2 + (x^2 + 2xy + y^2) = ??$$

3. anonymous

@Nixy so I'm literally just adding them together? It's just $(x+y)^{2} + (x^{2} + 2xy + y^{2})$ ?

4. anonymous

Yes. An identity is an equation that is always true. Once you solve by adding them together and put it on the other side of the = you will have an equation that is always true (identity)

5. anonymous

For example. $$\huge \frac{a}{2} = a × 0.5$$ is an identitiy and is always true

6. anonymous

so for the example you gave me, am I supposed to use the distributive property then?

7. anonymous

i mean, for the first example

8. anonymous

You need to expand this first (x+y)^2 and then add all like terms

9. anonymous

Expand $$\huge(x+y)^2$$ and then add all like terms

10. anonymous

so, expanding (x+y)^2 $(x+y) \times (x+y)$ right?

11. anonymous

$$\huge (x+y)(x+y) = ???$$ is correct

12. anonymous

Now times them using foil

13. anonymous

x^2 + xy^2 + y^2 ?

14. anonymous

So we have $$\huge x^2 + 2xy + y^2$$

15. anonymous

Now we have $$\huge x^2 + 2xy + y^2 + x^2 + 2xy + y^2$$ combine all like terms now.

16. anonymous

17. anonymous

x^4 + 4xy + y^4 ?

18. anonymous

We should have $$\huge 2x^2+4xy+2y^2$$ You don't add the exponents x^2 + x^2 = 2x^2

19. anonymous

So we have an identity now and no matter what value we use for x or y is always true.. Below is our identity So we have an identity below now. $$\large (x+y)^{2} + (x^{2} + 2xy + y^{2}) = 2x^2+4xy+2y^2$$

20. anonymous

Thank you so much for helping me, I'm actually understanding it a lot better now.

21. anonymous

You can combine them in all types of ways to make an identity

22. anonymous

You can subtract, divide, times, add and square them. They can get pretty complex or they can be simple. Any questions?

23. anonymous

I think I've got it, thank you c:

24. anonymous

YW, time for me to get to bed :-) Almost 12 AM here :-)

25. anonymous

Haha, same here. This is part of my last assignment, and I just wanted to get it done right! Thanks again for all your help. You're a lifesaver.