Question

PLEASE HELP< IM LOST: DETAILS BELOW ALGEBRA QUESTION PLZ HELP

Answer 1

@CoolDude12 @imqwerty @pooja195 @triciaal

Answer 2

what grade are you in?

Answer 3

Sophomore

Answer 4

what is that?

Answer 5

10th grade of high school

Answer 6

oh

Answer 7

sorry i cant help you im only in 6th grade

Answer 8

@YoungStudier @imqwerty please help

Answer 9

@phi

Answer 10

It sounds like they gave you a list of expressions in column A and column B

pick one of the expressions from column A
what is it ?

Answer 11

you should choose one from column A

Answer 12

ok so (x+y)

Answer 13

now square it. that means multiply it by itself
(x+y)(x+y)
if you don't know how, this explains it:
https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/multiplying-binomials-core-algebra/v/multiplying-binomials

Answer 14

so I would get x^2+xy+yx+y^2? @phi

Answer 15

yes, and yx is the same as xy (yx means y times x, and we can switch the order when multiplying)
also xy+xy means we have 2 xy's and people would combine them to just 2xy
so the answer is
x^2 +2xy+y^2

Answer 16

i really need help with the whole process please if you could

Answer 17

you could write it 2yx but generally people write the variables in alphabetical order (just a convention)

Answer 18

they want you to
add it to one factor from column B

so pick an expression from column B

Answer 19

ok (ax+b)

Answer 20

add it
x^2 +2xy+y^2 + ax + b

which can be written in this order
x^2 +ax+ 2xy+y^2 + b

Answer 21

ok so how would i add those all together to make it coherent

Answer 22

is that it written already combined?

Answer 23

you can't do anything more , unless we have numbers for a and b

I am not sure what they want out of this exercise.
what you have shown is
(x+y)^2 + ax+b = x^2 +ax + 2xy + y^2 + b

Answer 24

ok so would my final answer just be : x^2 +ax+ 2xy+y^2 + b?

Answer 25

yes

Answer 26

can you make a photo or screen shot of the original problem ?

Answer 27

What I am trying to figure out is if we can replace a and b with numbers.
for example use (2x+3) (with a=2 and b=3)
then your answer would be
(x+y)^2 + 2x+3 = x^2 +2x + 2xy + y^2 + 3

now we can show this identity works for different x and y values
for example, for (0,0) we get
(0+0)^2 + 2*0 + 3 = 0^2 +2*0 +2*0*0 + 0^2 + 3
3 = 3

they want you to show that for a few (x,y) pairs of numbers.

Answer 28

I think that is what
Demonstrate that your polynomial identity works on numerical relationships
is what that means

Answer 29

For this part
Prove that it is true through an algebraic proof, identifying each step

write the starting expression
(x+y)^2 + 2x+3
and show your work for squaring (x+y) and then adding 2x+3

Answer 30

ok! so what do I need to do to get my composite final answer as a whole??

Answer 31

what do you mean?

Answer 32

what would I write as my final answer(s) for the project? How would I put together my answer for this project

Answer 33

design an advertisement for a new polynomial identity

you are supposed to make a flyer or advertisement selling your identity

your identity is
(x+y)^2 + 2x+3 = x^2 + 2x + 2xy + y^2 + 3

you should put in some lines that say it works:
show the algebra to show the left side becomes the right side

then put in some numbers for x and y and show both sides simplify to the same number.

Answer 34

and what algebraic proof can I use to show that it works???

Answer 35

A long ago people sold "pet rocks"
see https://en.wikipedia.org/wiki/Pet_Rock

if you can sell a rock as a pet, you can sell anything.

I guess you should think of the expression as valuable information, that people would buy if they thought it was true, and then explain how it is true.

Answer 36

algebraic proof

that would just be the algebra you used to multiply out
(x+y)^2
and then add 2x+3 (which is not hard, you just "tack" those terms onto the the first part)

Answer 37

how exactly do I show that in a proof though?

Answer 38

im not sure how to show each step

Answer 39

you could do this
(x+y)^2 = (x+y)(x+y) reason: definition of exponent 2
(x+y)(x+y)= x(x+y) + y(x+y) reason: distributive law of multiplication over addition
x(x+y) = x^2 + xy reason: same as above
y(x+y) = yx+ y^2 reason: as above
therefore
(x+y)(x+y)= x^2 + xy+yx + y^2 reason: substitution
yx= xy reason: commutative law of multiplication
therefore
x^2 + xy+yx + y^2 = x^2 + xy+xy + y^2 reason: substitution
= x^2 +2xy + y^2 reason: addition of like terms
and so
(x+y)^2 = x^2 +2xy + y^2 reason: rules of algebra

Answer 40

and finally
(x+y)^2 +2x+3 = x^2 + 2x + 2xy+y^2 + 3 reason: addition of equal terms to both sides

Answer 41

so is this on algebraic proof: x^2 + xy+yx + y^2 = x^2 + xy+xy + y^2 reason: substitution
= x^2 +2xy + y^2 reason: addition of like terms
and so
(x+y)^2 = x^2 +2xy + y^2 reason: rules of algebra

Answer 42

yes, but you have to start with
(x+y)^2

Answer 43

you could say
(x+y)(x+y)= x^2 + xy+yx+y^2 reason: multiplication of two binomials

that is not really a law of arithmetic (like the commutative or distributive laws)
but you probably can get away with it. In the other post I showed how we can use the distributive law to do the multiplication.

Answer 44

@phi