Question

polynomial identities help! will medal

Answer 1

You have been hired as an efficiency expert for Math Nerds Inc. The company wants to cut costs and increase profits by increasing the number of math problems their employees can solve in a day. Your job is to help the Math Nerds employees solve math problems more quickly.

Answer 2

Show the Math Nerds employees how to rework each problem below using a polynomial identity.

Time yourself working the problem the long way. Then time your self working the problem using a polynomial identity. Show the Math Nerds employees how much time you save on each problem by using the polynomial identity to simplify.

Answer 3

1) ( x+2 )^2 or (x+2) ^2 = (x+y) ^2 = x ^2 +2xy+ y^ 2



2) ( x−3 )^3 or (x−3)^3 = (x−y) ^3 = x ^3 −3 x^ 2 y+3x y^ 2 − y^ 3

Answer 4

@satellite73

Answer 5

can you help me? its part of a project an my teacher is frustrated with me because i dont understand it lol

Answer 6

which defeats the purpose of being a teacher lol

Answer 7

me neither but we can try

Answer 8

i think the idea is this
this is an identity \[ (x+y) ^2 = x ^2 +2xy+ y^ 2\]

Answer 9

ok i tried solving it and she said no pluging in triples just work it out like it is. and im like >_< what

Answer 10

ok

Answer 11

so instead of computing
\[(x+2)^2\] by writing
\[(x+2)^2=(x+2)(x+2)=x^2+2x+2x+4=x^2+4x+4\] you can just say it looks like
\[(x+y)^2\] with \[y=2\] and go right to the answer
\[(x+2)^2=x^2+2\times 2x+2^2=x^2+4x+4\]

Answer 12

multiply polynomials! And you NEVER distribute the exponent across addition or subtraction like you did. Think about what an exponent means, then expand it (get rid of it by using the definition!) she said this and something about the FOIL method

Answer 13

wait the last one is the answer to the 2nd part?

Answer 14

lets go slow you are confused, me a little too, but you more so

Answer 15

i will bet that when your teacher wrote this :
"And you NEVER distribute the exponent across addition or subtraction like you did"
it is because you did something like say
\[(x+2)^2=x^2+4\]

Answer 16

well for (x+2)^2 i did x(x+4)+4 lol

Answer 17

actually that will work,

Answer 18

but your final answer should look like \(x^2+4x+4\)

Answer 19

oh for the (x+2)^2?

Answer 20

yes

Answer 21

oh ok

Answer 22

now lets get back to that first problem and figure out exactly what your teacher wants you to say

Answer 23

slowly

Answer 24

ok lol

Answer 25

this is a "polynomial identity"
\[(x+y) ^2 = x ^2 +2xy+ y^ 2\]

Answer 26

if you can open that it should be the last page

Answer 27

so in order to find
\[(x+2)^2\] without writing \((x+2)(x+2)=x^2+2x+2x+4=x^2+4x+4\) instead say \(y=2\) and use the identity to get
\[x^2+2\times 2x+2^2=x^2+4x+4\] quicker
that is the answer to the first question

Answer 28

ok

Answer 29

so plug in 2 for y in that formula?

Answer 30

yes, i wrote what you get above

Answer 31

same for the last one

Answer 32

ok

Answer 33

can you open the file?

Answer 34

you have
\[(x-3)^3\] and instead of writing \\[(x-3)(x-3)(x-3)\] you use the identity
\[(x-y)^3=x^3-3x^2y+3xy^2-y^3\]

Answer 35

where you see an \(x\) put an \(x\) and where you see a \(y\) put a \(3\)

Answer 36

so \[(x+2)^2=x^2+2x2x+2^2=x^2+4x+4 \]

Answer 37

Satellite plz help me when ur done thanks

Answer 38

\[(x+2)^2=x^2+2\times 2x+2^2=x^2+4x+4\]

Answer 39

thats for the (x+2)^2

Answer 40

yes

Answer 41

for (x-3)^3 i got \[(x-3)^3=x^3-3x^23+3x3^3-3^3\]

Answer 42

math is not kind to me lol

Answer 43

yeas that is right! then compute the numbers

Answer 44

i solve that?

Answer 45

\[x^3-9x^2+27x+27\]

Answer 46

oh. -_- lol

Answer 47

so what about the 2nd part on 1.?

Answer 48

where (x+2)^2=(x+y)^2=x^2+2xy+y^2

Answer 49

@satellite73

Answer 50

site is messing up sorry

Answer 51

its ok

Answer 52

look i didn't write this it is stupid and there is no wonder you are confused, because it doesn't make sense
that thing you just wrote it nonsense, some idiot wrote this sheet

Answer 53

just write \[(x+2)^2=x^2+4x+4\] and be done with it

Answer 54

ok

Answer 55

well thanks

Answer 56

good luck sorry the work sheet is so bad, but at least we got the right answers

Answer 57

yeah lol