anonymous
  • anonymous
will fan and medal~ polynomials and identities ~ Basically I have an assignment where I need to make my own polynomial identity
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • 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)
anonymous
  • 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 \( (x + y)^2 + (x^2 + 2xy + y^2) = ?? \)
anonymous
  • anonymous
@Nixy so I'm literally just adding them together? It's just \[(x+y)^{2} + (x^{2} + 2xy + y^{2})\] ?

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anonymous
  • 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)
anonymous
  • anonymous
For example. \( \huge \frac{a}{2} = a × 0.5 \) is an identitiy and is always true
anonymous
  • anonymous
so for the example you gave me, am I supposed to use the distributive property then?
anonymous
  • anonymous
i mean, for the first example
anonymous
  • anonymous
You need to expand this first (x+y)^2 and then add all like terms
anonymous
  • anonymous
Expand \( \huge(x+y)^2 \) and then add all like terms
anonymous
  • anonymous
so, expanding (x+y)^2 \[(x+y) \times (x+y)\] right?
anonymous
  • anonymous
\( \huge (x+y)(x+y) = ???\) is correct
anonymous
  • anonymous
Now times them using foil
anonymous
  • anonymous
x^2 + xy^2 + y^2 ?
anonymous
  • anonymous
So we have \( \huge x^2 + 2xy + y^2 \)
anonymous
  • anonymous
Now we have \( \huge x^2 + 2xy + y^2 + x^2 + 2xy + y^2 \) combine all like terms now.
anonymous
  • anonymous
Add all terms that can be added together.
anonymous
  • anonymous
x^4 + 4xy + y^4 ?
anonymous
  • anonymous
We should have \( \huge 2x^2+4xy+2y^2 \) You don't add the exponents x^2 + x^2 = 2x^2
anonymous
  • 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. \( \large (x+y)^{2} + (x^{2} + 2xy + y^{2}) = 2x^2+4xy+2y^2 \)
anonymous
  • anonymous
Thank you so much for helping me, I'm actually understanding it a lot better now.
anonymous
  • anonymous
You can combine them in all types of ways to make an identity
anonymous
  • anonymous
You can subtract, divide, times, add and square them. They can get pretty complex or they can be simple. Any questions?
anonymous
  • anonymous
I think I've got it, thank you c:
anonymous
  • anonymous
YW, time for me to get to bed :-) Almost 12 AM here :-)
anonymous
  • 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.

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