Question

Multiply, using any appropriate method. (3-a)^3

Answer 1

Writing this out and then FOILing might helping you.

this can be rewritten as \[(3-a) * (3-a) * (3-a)\]

Then just FOIL the first two together so (3-a) * (3-a), after you've found that, multiply it by the last (3-a).

Are you familiar with FOIL? (First, Outer, Inner, Last)

Answer 2

I am familiar with it but it gets me really lost

Answer 3

ok, to FOIL (3-a) * (3-a)

F(irst) - multiply the first term in each expression: 3*3... so we have 9.

O(uter) - we multiply the terms that are on the outside edges. That would be 3 * -a, which is just -3a.

I(nner) - we multiply the two inside terms. -a*3. Another -3a.

L(ast) - multiply the last term in each expression. a*a = a^2

Answer 4

Now put those terms together. we have a 9 - 3a - 3a - a^2. Combine the 3a's and you've got \[9 - 6a - a^2\]

Answer 5

Now just multiply that by the remaining (3-a) , you will have to combine a few terms, then your done!

Answer 6

Do it one step at a time. You've got \[(3-a)^3=(3-a)(3-a)(3-a)\]Tackle just a pair of \((3-a)\)'s first, then multiply the result by another \((3-a)\) for the whole thing.

\[(3-a)(3-a) = 3(3-a) - a(3-a)\]by distributive property
Now do that again
\[3(3-a)-a(3-a) = 3*3-3*a-a*3-a*(-a) \]\[= 9-3a-3a+a^2\]\[ = 9-6a+a^2\]
Now multiply that by \((3-a)\) to get \((3-a)^3\)
\[(3-a)(9-6a+a^2) = 3(9-6a+a^2) -a(9-6a+a^2) \]\[= 3*9-3*6a+3*a^2-a*9-a(-6a)-a*a^2 \]\[= 27-18a + 3a^2-9a+6a^2-a^3\]\[=-a^3+9a^2-27a+27\]

Answer 7

ok now I am really lost because I did what you said and when I put it in it said that it was wrong the correct answer was \[1-3a+3a ^{2}-a ^{3}\]

Answer 8

how did they come up with that answer. I am so lost on trying to figure this out

Answer 9

Im not sure, while I don't think its a good idea to give an answer, the answer whpalmer4 gave you is 100% correct.

Answer 10

ok can you walk me through doing \[(4-3a)^{3}\]

Answer 11

Was there something missing from what you gave us to begin with? Or was the problem simply \[3-a)^3\]

Answer 12

this is the same basic idea as above. If you replace the 3 with a 4, and the "a" with a "3a" and follow the steps, you will get the right answer.

Answer 13

The problem for which \[1-3a+3a^2-a^3\] is the correct answer is \((1-a)^3\)

Answer 14

write it as \[(4-3a) * (4-3a) * (4-3a)\]

and just work on a piece at a time.

Answer 15

ok this is what I have for the first two steps

Answer 16

@xartaan as for giving the answer, I know she's got a ton of these to do, so she's not going to get any appreciable advantage from my having worked one through to the end, except seeing how to do it.

Answer 17

\[(4-3a)^{3}=(4-3a)(4-3a)(4-3a)\]
\[(4-3a)(4-3a)=4(4-3a)-a(4-3a)\]

Answer 18

@xartaan the code of conduct says we are to guide them — she's being guided through the process. if she was just an answer seeker, she wouldn't have hung in there this long!

Answer 19

@cahayes9498 that's very close, except you turned the 3a into a at the end...
\[(4-3a)(4-3a) = 4(4-3a)-3a(4-3a)\] see the difference?

Answer 20

then \[4(4-3a)-3a(4-3a)=4*4-4*3a-3a*4-3a*(-3a)\]

Answer 21

yeah I noticed that after wards I corrected it

Answer 22

good eyes!

Answer 23

looks good so far, now simplify

Answer 24

now \[4*4-4*3a-3a*4-3a*(-3a)=16-12a-12+3a ^{2}\]

Answer 25

whoops, another typo in there...

Answer 26

only one constant term per multiplication!

Answer 27

huh? :(

Answer 28

\[16-12a-12+3a ^{2}=16-24a+3a ^{2}\]

Answer 29

\[=4(16-24a+3a ^{2})-3a(16-24a+3a ^{2})\]

Answer 30

ok this is where I start to really get confused

Answer 31

\[4*16+4*24a+4*3a ^{2}-3a ^{2}*16-3a ^{2}(-24a)-3a*3a ^{2}\]
is the next thing that I got

Answer 32

@whpalmer4 you still there

Answer 33

I am now! :-)

Answer 34

ok great

Answer 35

am I correct so far?

Answer 36

\[16-12a-12+3a^2 \ne 16-24a+3a^2\]but
\[16-12a-12a+3a^3=16-24a+3a^2\]

Answer 37

and the latter is what you wanted, you just dropped an a again

Answer 38

have to be fastidious when doing this work!

Answer 39

so now you have \((4-3a)^2 = 16-24a+3a^2\) and you have to multiply that by one more \((4-3a)\) in order to get \((4-3a)^3\)

\[(4-3a)(16-24a+3a^2)=\]

your turn :-)

Answer 40

oh, and I see you already did that...now can you simplify?

Answer 41

except you lost a minus sign in front of -24a when you multiplied :-(

Answer 42

so it would be \[4*16+4*24a+4*3a ^{2}-3a ^{2}*16-3a ^{2}*24a-3a+3a ^{2}\]

Answer 43

which would simplify to \[64+96a+12a ^{2}-48a ^{2}-72a ^{2}-3a+3a ^{2}\]

Answer 44

this is the part that I get so lost with and dont understand how to simplify it the correct way

Answer 45

okay, the problem is you aren't doing the multiplication correctly, so it doesn't matter if you can simplify correctly :-)

Answer 46

Let's look at just the first half:

\[(4-3a)(16-24a+3a^2) = 4(16-24a+3a^2) + (\text{the rest})\]\[4(16-24a+3a^2) = 4*16-4*24a + 4*3a^2 + (\text{the rest})\]
Look carefully at what I have there vs. what you have there...

Answer 47

ok I see that I added when I should have subtracted

Answer 48

Yeah, you didn't apply the - negative sign when multiplying 4 * -24a...

Answer 49

ok so from here I would do 4*16 which is 64

Answer 50

you made the corresponding mistake in the other half, too, it appears...

Answer 51

why don't you write out the last line for me again, the practice would be good...

Answer 52

\[4*16+4*24a+4*3a ^{2}-3a ^{2}*16+3a ^{2}*24a-3a+3a ^{2}\]

Answer 53

is that correct?

Answer 54

no, you keep forgetting to include the negative signs!

\[4(16-24a+3a^2) = 4*16 + 4*(-24a) + 4*3a^2 = 64-96a+12a^2\]

Answer 55

in the second part?

Answer 56

no, in the first part. you always write \[4*16+4*24a+4*3a^2\]but it is \[4*16\color{red}{-}4*24a+4+3a^2\]

Answer 57

I am never going to get this

Answer 58

well thank you for trying to help me I am just going to get this one wrong I am never going to figure this out I get so confused with it.

Answer 59

no, there's no reason to get this wrong.

\[4(x-a) = 4*x + 4*(-a) = 4x-4a\]

\[4(x+a) = 4*x + 4*a = 4x+4a\]

Answer 60

you're getting the trickier parts right, and getting tripped up an a relatively easy part :-)

Answer 61

\[4(16-24a+3a^2) = 4*16 + 4*(-24a) + 4*3a^2\]\[=64-96a+12a^2\]

Answer 62

you just can't drop that - sign in front of 24a...

Answer 63

I just dont understand why it cant be \[(4-3a)^{3} = (1a)^{3}\]

Answer 64

the sign is part of the number. maybe it would help to write it out whatever sign it is:
\[4(16-24a+3a^2) = 4*(+16)+ 4*(-24a) + 4(+3a^2) = 64 + (-96a) + 12a^2 \]\[=64-96a+12a^2\]

Answer 65

ok I understand that part now but the rest of it all is making my head explode

Answer 66

because \(4-3a \ne 1a\) for most values of \(a\). What if \(a=0\)?
\[4-3(0) = 1*0\]\[4=0\]Uh, no.

Answer 67

I know that it dont equal that I was just wishing it would be that simple

Answer 68

Think about numbers. 169 = 1*100 + 6*10 + 9*1, right?
well, this is the same thing, except instead of powers of 10, we have powers of \(a\).

Answer 69

\[4-3a\] is really \[-3a + 4 = -3a^1+4a^0\]because \(a^1=a\) and \(a^0=1\) (so long as \(a\ne 0\), as \(0^0\)is undefined)

Answer 70

ok i got the first part of it with the \[64-96a+12a ^{2}\] now the rest of it that I came up with which is probably wrong is \[-16a+24a ^{2}-3a ^{3}\] so all together I got \[64-96a+12a ^{2}-16a+24a ^{2}-3a ^{3}\]

Answer 71

let's see\[-3a(16-24a+3a^2) = -48a+72a^2-9a^3\]looks like you left off the 3...

Answer 72

all together you should have \[64-96a+12a^2 -48a +72a^2-9a^3\]Can you simplify that by collecting like terms?

Answer 73

ok so the second part I just had to multiply everything by the 3a?

Answer 74

by the -3a...

Answer 75

oh ok that makes sense now

Answer 76

so now I would just combine like terms

Answer 77

would it be \[64-144a+84a ^{2}-9a ^{3}\]

Answer 78

crap, we've been carrying an error all along, I think. let's go from the start:

\[(4-3a)(4-3a) = 4(4-3a) -3a(4-3a) = 4*4-4*3a-3a*4+9a^2 \]\[= 16-24a+9a^2\]
Now we multiply again by \((4-3a)\):
\[(4-3a)(16-24a+9a^2) = 4(16-24a+9a^2)-3a(16-24a+9a^2)\]\[= 4*16-4*24a+4*9a^2 -3a*16 -3a*(-24a)-3a*9a^2\]\[=64-96a+36a^2-48a+72a^2-27a^3\]

Answer 79

you correctly simplified an incorrect equation :-) good job by you, poor job by me

Answer 80

This last one is correct, I promise!

Answer 81

so what I got was not right

Answer 82

you simplified what you had in front of you correctly. I'm not sure whose fault it is that what you had to simplify was not correct. I should have spotted the mistake earlier

Answer 83

\[64-144a+108a ^{2}-27a ^{3}\]

Answer 84

yes!!!!!! :-)

Answer 85

how about that, with the correction made

Answer 86

go me.... its my birthday.... LOL

Answer 87

you deserve a medal for hanging in there :-)

Answer 88

and i have the subtract and add correct?

Answer 89

happy birthday to you, happy birthday to you...how old? double digits yet? :-)

Answer 90

not really my birthday just a saying in florida sorry

Answer 91

that answer is exactly correct.

Answer 92

ok good, i am glad I didnt quit

Answer 93

hey, no one is checking IDs here, if you say it's your birthday, it's your birthday :-)

Answer 94

thank you for being so patient with me and helping me to figure this out

Answer 95

free drinks on the house! help yourself to anything in the refrigerator :-)

Answer 96

lol.... I am going to help myself to the bed.... Im too old should have been in bed a long time ago

Answer 97

you're welcome! this is the sort of thing where it's puzzling until you have that little breakthrough, and then you wonder why it was such a big problem...