Question

will fan and medal~
polynomials and identities ~

Basically I have an assignment where I need to make my own polynomial identity

Answer 1

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)

Answer 2

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

\( (x + y)^2 + (x^2 + 2xy + y^2) = ?? \)

Answer 3

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

Answer 4

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)

Answer 5

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

Answer 6

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

Answer 7

i mean, for the first example

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Now times them using foil

Answer 13

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

Answer 14

So we have \( \huge x^2 + 2xy + y^2 \)

Answer 15

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

Answer 16

Add all terms that can be added together.

Answer 17

x^4 + 4xy + y^4 ?

Answer 18

We should have \( \huge 2x^2+4xy+2y^2 \)

You don't add the exponents x^2 + x^2 = 2x^2

Answer 19

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.

\( \large (x+y)^{2} + (x^{2} + 2xy + y^{2}) = 2x^2+4xy+2y^2 \)

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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.