anonymous
  • anonymous
.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[(5x^2 + 3x + 4) − (2x^2 − 6x + 3)\]distribute the minus sign and get \[5x^2 + 3x + 4 -2x^2 + 6x - 3)\]
anonymous
  • anonymous
since you are only asked for B you job is to compute \(3+6\)
anonymous
  • anonymous
yes

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jim_thompson5910
  • jim_thompson5910
Add up 3x^2 - 9 and 2x + 9 So (3x^2 - 9) + (2x + 9) = ???
anonymous
  • anonymous
5x^2 ?
jim_thompson5910
  • jim_thompson5910
Sorry, I didn't see the first x Add x, 3x^2 - 9 and 2x+9 (x) + (3x^2 - 9) + (2x + 9) x + 3x^2 - 9 + 2x + 9 3x^2 + 3x + 0 3x^2 + 3x
jim_thompson5910
  • jim_thompson5910
So after adding x, 3x^2 - 9 and 2x + 9, you will get 3x^2 + 3x, which is the total distance covered
anonymous
  • anonymous
soo its 3x^2 + 3x
anonymous
  • anonymous
add them up \[x+3x^2 - 9+2x + 9\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
thanks!
anonymous
  • anonymous
they really reach for these "word problems" don't they ?
anonymous
  • anonymous
they could have said "add the polynomials"
anonymous
  • anonymous
LOLLL yess they do !! Can you guys do me onee more favor and just double check my work ?
jim_thompson5910
  • jim_thompson5910
sure, what do you need to check
anonymous
  • anonymous
ill write the 5 questions and show you my answers
anonymous
  • anonymous
1. Simplify the following expression: (x − 8y) - (2x − 4y)If the final answer is written in the form Ax + By, what is the value of B? 2. Simplify: (4x − 6) − (5x + 1) 3. Simplify: (5x^2 + 3x + 4) + (5x^2 + 5x − 1) 4. Simplify: (4x − 6) + (3x + 6) & You helped me with the other 2 questions so i just put the ones i did on my own but these were my answers 1. 4y 2. -x-7 3. 10x^2 + 8x + 5 4. 7x+12
jim_thompson5910
  • jim_thompson5910
ok one sec
anonymous
  • anonymous
alrighty :] Thanks!!
jim_thompson5910
  • jim_thompson5910
#1 the form is form Ax + By they want the value of B, so the answer cannot be 4y
jim_thompson5910
  • jim_thompson5910
besides, -8y + 4y isn't 4y anyway you lost a sign somewhere
anonymous
  • anonymous
Im bad with my signs /: negatives and positives -.- so confusing
jim_thompson5910
  • jim_thompson5910
think of it like this -8 + 4 is the same as saying you're 8 dollars in debt, but you paid off $4 of that debt, so you're now 4 dollars in debt
jim_thompson5910
  • jim_thompson5910
so that explains how -8 + 4 = -4
jim_thompson5910
  • jim_thompson5910
and why -8y + 4y = -4y
anonymous
  • anonymous
so itd be -4?
jim_thompson5910
  • jim_thompson5910
B is -4, yep
anonymous
  • anonymous
oki
jim_thompson5910
  • jim_thompson5910
# 2 is correct, so congrats on that
anonymous
  • anonymous
thanks :]
jim_thompson5910
  • jim_thompson5910
#3 is close
jim_thompson5910
  • jim_thompson5910
but not correct fully
jim_thompson5910
  • jim_thompson5910
4 + (-1) is NOT 5
anonymous
  • anonymous
-3?
jim_thompson5910
  • jim_thompson5910
you have 4 dollars you add on 1 IOU
jim_thompson5910
  • jim_thompson5910
you really have 4-1 = 3 dollars left (after you pay off the IOU)
jim_thompson5910
  • jim_thompson5910
so that's why 4 + (-1) = 4 - 1 = 3
anonymous
  • anonymous
oh alright ! i get it now.
jim_thompson5910
  • jim_thompson5910
ok great
jim_thompson5910
  • jim_thompson5910
# 4 is also incorrect
anonymous
  • anonymous
sorry im blonde it takes a little bit.
jim_thompson5910
  • jim_thompson5910
that's ok, just practice practice practice and hair color is just skin deep...has nothing to do with intelligence
anonymous
  • anonymous
Lol yeah , im guessing #4 is 7x-12
jim_thompson5910
  • jim_thompson5910
-6 + 6 = ???
jim_thompson5910
  • jim_thompson5910
-6 means you are $6 in debt add on $6, so you are paying off $6 are you still in debt?
anonymous
  • anonymous
nope itd be zero :o
jim_thompson5910
  • jim_thompson5910
yep
jim_thompson5910
  • jim_thompson5910
-6+6 = 0
anonymous
  • anonymous
so the answers just 7x?
jim_thompson5910
  • jim_thompson5910
so you'd have 7x+0 or just 7x
jim_thompson5910
  • jim_thompson5910
you got it
anonymous
  • anonymous
ok aha :]
jim_thompson5910
  • jim_thompson5910
just watch out for the signs and try not to forget any
anonymous
  • anonymous
Ill think of the whole dollar thing next time i come to the signs , Thank you so much ! ! :]
jim_thompson5910
  • jim_thompson5910
that's how I grasp negatives when I stumble a bit, and you're welcome
anonymous
  • anonymous
Ive always troubled negatives , ive been taking algebra 1 for 3 years now , and havent passed . Im working so much harder now ,
jim_thompson5910
  • jim_thompson5910
have you thought of using money terms for negatives before? I'm just curious how your teachers have taught negatives in the past
anonymous
  • anonymous
ive heard of it but it was never enforced.
jim_thompson5910
  • jim_thompson5910
I gotcha, so they brought it up (maybe once or twice), but never really stuck to it
anonymous
  • anonymous
nopeeeee
anonymous
  • anonymous
Im trying to finish up my work for next week so im ahead so i can spend my spring break with my younger sister , would you mind helping me with Multiplying monomials?
jim_thompson5910
  • jim_thompson5910
sure I can help
anonymous
  • anonymous
Choose the correct simplification of the expression d^3 • d^5. d d^15 d^2 d^8
jim_thompson5910
  • jim_thompson5910
what did you get
anonymous
  • anonymous
the arrow represents the degree of the monomials incase you didnt already know lol. and i think its d^15??
jim_thompson5910
  • jim_thompson5910
^ means exponents, yes I know and no it's not d^15
jim_thompson5910
  • jim_thompson5910
if you are multiplying expressions with the same base, then you add the corresponding exponents
jim_thompson5910
  • jim_thompson5910
example x^2 times x^3 = x^(2+3) = x^5
anonymous
  • anonymous
Alright that sounds a little better so d^8 ?
jim_thompson5910
  • jim_thompson5910
because you can expand out the 'x' terms and you'll see 5 total x terms
jim_thompson5910
  • jim_thompson5910
yep d^8
anonymous
  • anonymous
alright you make this so much easier than the lesson lol
jim_thompson5910
  • jim_thompson5910
lol glad to hear that
jim_thompson5910
  • jim_thompson5910
glad it's finally clicking
anonymous
  • anonymous
Choose the correct simplification of the expression (b^5)^4. b^9 b^625 b^20 b
anonymous
  • anonymous
b^20 ?
jim_thompson5910
  • jim_thompson5910
you got ???
jim_thompson5910
  • jim_thompson5910
perfect
jim_thompson5910
  • jim_thompson5910
you're a total pro at this
anonymous
  • anonymous
HA i wish!
jim_thompson5910
  • jim_thompson5910
you're just not giving yourself enough credit
anonymous
  • anonymous
Choose the correct simplification of the expression (3x)^4. 81x^4 12x^5 81x^5 12x^4
jim_thompson5910
  • jim_thompson5910
raise each piece to the 4th power
anonymous
  • anonymous
81x^4 ?
jim_thompson5910
  • jim_thompson5910
so you raise 3 to the 4th power to get ____
jim_thompson5910
  • jim_thompson5910
yep, you got it
jim_thompson5910
  • jim_thompson5910
see you know this stuff
anonymous
  • anonymous
haha slowly but getting it !! :)
jim_thompson5910
  • jim_thompson5910
well as long as you get there, that's all that matters
anonymous
  • anonymous
Choose the correct simplification of the expression (x^2y)^2. x^4y^3 x^6y^6 x^4y^2 xy^4
jim_thompson5910
  • jim_thompson5910
what did you get
anonymous
  • anonymous
Havent even tried it yet lol .but im thinking the ^2 on the outside is going to distribute to the ones in the parenthese?
jim_thompson5910
  • jim_thompson5910
yes that's one way of thinking about it basically you raise each part to the 2nd power
jim_thompson5910
  • jim_thompson5910
x^2 to the 2nd power ----> x^2 * x^2 = x^(2+2) = x^4
jim_thompson5910
  • jim_thompson5910
y to the second power -----> y^2
jim_thompson5910
  • jim_thompson5910
or you can multiply the exponents multiply the outer by each of the inner
anonymous
  • anonymous
so x^4y^2
jim_thompson5910
  • jim_thompson5910
yep
anonymous
  • anonymous
:] this isnt so hard
jim_thompson5910
  • jim_thompson5910
no, it's not at all just depends on how much practice you have and how you look at it
anonymous
  • anonymous
Choose the correct simplification of the expression b^5 • b^4. b b^9 b^20 b^−1
jim_thompson5910
  • jim_thompson5910
you got _____
anonymous
  • anonymous
b^9 ?
jim_thompson5910
  • jim_thompson5910
correct
anonymous
  • anonymous
:DD !!
jim_thompson5910
  • jim_thompson5910
you add the exponents I'll brb
anonymous
  • anonymous
3 more ,
anonymous
  • anonymous
ok sounds good.
jim_thompson5910
  • jim_thompson5910
no worries I'll be back in a few min and I'll help you with those 3
anonymous
  • anonymous
Okay :D
jim_thompson5910
  • jim_thompson5910
ok back
anonymous
  • anonymous
Choose the correct simplification of the expression (d3)^5. d^8 d^15 d^243 d
anonymous
  • anonymous
d^15 right ?
jim_thompson5910
  • jim_thompson5910
correct, assuming you mean (d^3)^5
anonymous
  • anonymous
yes sorry i forgot the ^ x]
jim_thompson5910
  • jim_thompson5910
no worries
anonymous
  • anonymous
okay these last 3 .
anonymous
  • anonymous
heres 2 of the 3
1 Attachment
jim_thompson5910
  • jim_thompson5910
and you got what for each
anonymous
  • anonymous
How do i simplify them ?
anonymous
  • anonymous
just add the exponents?
jim_thompson5910
  • jim_thompson5910
(3d)^3 turns into 27d^3
jim_thompson5910
  • jim_thompson5910
so (3d)^3 * d becomes 27d^3 * d
jim_thompson5910
  • jim_thompson5910
and that becomes what?
anonymous
  • anonymous
um. 27d^4 ?
jim_thompson5910
  • jim_thompson5910
good
anonymous
  • anonymous
alright i struggled a little bit
jim_thompson5910
  • jim_thompson5910
now simplify the other expression
jim_thompson5910
  • jim_thompson5910
that's ok, just keep practicing it and it'll come more easily to you
anonymous
  • anonymous
the second one the exponents are just gonna get added to each other right ?
jim_thompson5910
  • jim_thompson5910
no, when you square something that has an exponent, you are multiplying the exponents
jim_thompson5910
  • jim_thompson5910
ex: (3x^5)^2 ---> 9x^(5*2) = 9x^(10)
anonymous
  • anonymous
3d^4
jim_thompson5910
  • jim_thompson5910
so the exponents are different? or equal?
anonymous
  • anonymous
equal
jim_thompson5910
  • jim_thompson5910
so that means you go with C for the first one
jim_thompson5910
  • jim_thompson5910
exponents are the same
anonymous
  • anonymous
alright number 8 looks like mumbo jumbo...
jim_thompson5910
  • jim_thompson5910
same thing applies to #8, it's just a bit more complicated maybe
jim_thompson5910
  • jim_thompson5910
they want you to simplify as much as possible, then compare exponents for expressions 1 and 2
jim_thompson5910
  • jim_thompson5910
(2y^2)^3 = 8y^(2*3) = 8y^6
anonymous
  • anonymous
alright .
jim_thompson5910
  • jim_thompson5910
(y^9)*(2y^2)^3 turns into y^9 * 8y^6
anonymous
  • anonymous
what about that y^9
jim_thompson5910
  • jim_thompson5910
just added it back in so to speak
jim_thompson5910
  • jim_thompson5910
I focused on simplifying (2y^2)^3 first
jim_thompson5910
  • jim_thompson5910
then re-introduced the y^9 back in
anonymous
  • anonymous
okay so the first one you just add the like terms now right?
jim_thompson5910
  • jim_thompson5910
yep you add the exponents
anonymous
  • anonymous
y^9 * 8y^6 = 9y^15
jim_thompson5910
  • jim_thompson5910
the exponent is correct, but that 8 should stay the same
jim_thompson5910
  • jim_thompson5910
so it's 8y^15
jim_thompson5910
  • jim_thompson5910
silly typo though
anonymous
  • anonymous
alright so 8y^15 for the first one ,
jim_thompson5910
  • jim_thompson5910
now simplify the second one using the same steps
jim_thompson5910
  • jim_thompson5910
(2y^3)^2 = ???
anonymous
  • anonymous
4y^6
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
(9y)(2y^3)^2 becomes 9y*4y^6
anonymous
  • anonymous
13y^6
jim_thompson5910
  • jim_thompson5910
you multiply the coefficients out front
jim_thompson5910
  • jim_thompson5910
9*4 = 36
jim_thompson5910
  • jim_thompson5910
and you add the exponents 1+6 = 7
anonymous
  • anonymous
so 36y^7 ?
jim_thompson5910
  • jim_thompson5910
yep
anonymous
  • anonymous
that one was hard lol
jim_thompson5910
  • jim_thompson5910
now compare 8y^15 to 36y^7
jim_thompson5910
  • jim_thompson5910
its ok, it'll get easier over time
anonymous
  • anonymous
the first ones exponents are greater than
jim_thompson5910
  • jim_thompson5910
yep
anonymous
  • anonymous
Alright this is my last one .
jim_thompson5910
  • jim_thompson5910
so A
anonymous
  • anonymous
thank god
jim_thompson5910
  • jim_thompson5910
lol
anonymous
  • anonymous
Part 1: Explain, using complete sentences, how to simplify the expression below. Part 2: What is the simplified expression? (3x^3y^4)(2x^2y^6)
jim_thompson5910
  • jim_thompson5910
the coefficients are 3 and 2 what do you do with these?
anonymous
  • anonymous
multiply them
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
3 * 2 = 6 is your final coefficient
jim_thompson5910
  • jim_thompson5910
now for each variable, you add the corresponding exponents
anonymous
  • anonymous
so 6x^5 ?
jim_thompson5910
  • jim_thompson5910
so for the x terms, you add the exponents 3 and 2 to get 3+2 = 5 5 is the final exponent for x
jim_thompson5910
  • jim_thompson5910
so far so good, now do y
anonymous
  • anonymous
well y doesnt have any numbers but every variable is equal to 1 , so would it be 2y^10?
jim_thompson5910
  • jim_thompson5910
don't worry about the coefficient, that's been taken care of already
jim_thompson5910
  • jim_thompson5910
just focus on the exponents for y
anonymous
  • anonymous
so y^10 ?
jim_thompson5910
  • jim_thompson5910
they are 4 and 6, they add to 4+6 = 10
jim_thompson5910
  • jim_thompson5910
yep
jim_thompson5910
  • jim_thompson5910
so all together, we get 6x^5y^10
anonymous
  • anonymous
alright . so thats the simplied answer?
jim_thompson5910
  • jim_thompson5910
it is
anonymous
  • anonymous
that was easier lol
jim_thompson5910
  • jim_thompson5910
lol depends on how you look at it i guess
anonymous
  • anonymous
Thank you so much for all your time helping me tonight .
jim_thompson5910
  • jim_thompson5910
you're welcome

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