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Geek Culture / I need a little bit of math help

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Aaron Miller
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Posted: 3rd Oct 2008 01:31
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Long story short I need some help with my math homework. The book that they give out doesn't help much - in fact it barely does anything other than show examples.

I need to get at least 6 more questions right in order to be able to take the test (My teacher won't let me unless I take the test).

The questions are (And I will explain why I'm having trouble with 'em in a second):

Find the product.
10: (2k - 5)(3k + 2)
13: (m - 7)^2
Simplify. Write your answer using only positive exponents.
19: (5^4y^7) / (5^6y^3)
20: (8x)^-7(8x)^3
22: ((r^6s)^-2) / (r^-5s^3)
Perform each division.
24: (12x^4 - 6x^3 + 10x) / (3x^2)

Okay, now for the first one (Question 10) I'm having trouble because the book doesn't show anything about how to handle that. I've had questions similar to that one which have the same terms, but in the one above the coefficients are different - and no matter what I do the answer seems to be wrong (I replace k with some value - such as 5 and see if the answer I get from the question, and the answer I get from my answer to it is the same, if it's not then I know my answer is wrong). Mostly, I come up with this: 6k^2 - 10. But I know that's wrong.

For 13, none of the answers I provide are right - my teacher made a comment about it and told me to perform the problem for each term, but when I do that I just get m^2 - 7^2 which also seems to be wrong.

All the others are the same way - I'm doing the problems like the book says, but I'm messing up somewhere and can't figure out where - or perhaps I don't understand entirely. Anyways, these problems are different than the others and the book doesn't cover some of them, so I'm just wondering if someone could help me out, if they could explain what to do (Especially for number 10 - that one's bothering me), that'd be great.

Thanks for reading. I wouldn't ask help on my homework unless I really needed it.

Cheers,

-naota

I'm not a dictator to those that do stuff for me by will. Only those who don't.
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BiggAdd
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Posted: 3rd Oct 2008 01:50 Edited at: 3rd Oct 2008 02:06
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Here is what I get:

10. 6k^2 - 11k - 10
13. m^2 - 14m + 49

19. 5^(10y)
20. 1/(8x^(168x))
22. r^(3s)

24. 4x^2 - 2x + 10/3x



For 10 and 13, you are missing some of the products.

(a + b)^2 does not equal a^2 + b^2

(a + b)^2 = a^2 + 2ab + b^2

Or to expand it out into more letters:

(a + b)(c + d) = ac + ad + bc + bd




For 19, 20 and 22:

a^b * a^c = a^(b+c)

(a^b)^c = a^(bc)

a^b / a^c = a^(b-c)

Equally:
1/(a^b) = a^(-b)



For 24: (Break it up)
(12x^4) / (3x^2) = 4x^(4-2) = 4x^2 <- using the rule from before

(-6x^3) / (3x^2) = 2x^(3-2) = 2x

(10x) / (3x^2) = 10/3 * x^(1-2) = 10/3 * (x^-1) = 10/3x





Hope that Helps
(Hope I got it all right , If not I apologize!)

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Aaron Miller
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Posted: 3rd Oct 2008 02:17
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Thank you very much, it is much appreciated.

Cheers,

-naota

I'm not a dictator to those that do stuff for me by will. Only those who don't.
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JoelJ
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Posted: 3rd Oct 2008 02:17
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10: (2k - 5)(3k + 2)
13: (m - 7)^2

ok, here's what you do:

FOIL - First, outer, inner, last

so:
2k * 3k
2k * 2
-5 * 3k
-5 * 2
then you add like terms

you do the same with 13
(m - 7)(m - 7)


IntelCore2Duo@2.60GHz-4GB RAM-NVIDIA Quadro FX 570M-Windows Vista Business 32bit
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BiggAdd
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Posted: 3rd Oct 2008 11:05
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Quote: "Thank you very much, it is much appreciated. "


No problemo!

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Robert F
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Posted: 3rd Oct 2008 13:41 Edited at: 3rd Oct 2008 13:42
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Thats funny because we just learned how to do this stuff. It was on our Chapter 7 test.

Oh remember how to do FOIL, you will need it for the future.


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mamaji4
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Posted: 3rd Oct 2008 15:51
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Quote: "19: (5^4y^7) / (5^6y^3)
20: (8x)^-7(8x)^3
22: ((r^6s)^-2) / (r^-5s^3)"


@Aaron
I'm not sure whether you made a typo in writing the questions, but
they should read
19: ((5^4y)^7) / ((5^6y)^3)
20: ((8x)^-7(8x))^3
21: ((r^6s)^-2) / ((r^-5s)^3)

Or else you get totally different answers from what BigAdd has given.
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BiggAdd
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Posted: 3rd Oct 2008 18:20
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Quote: "@Aaron
I'm not sure whether you made a typo in writing the questions, but
they should read
19: ((5^4y)^7) / ((5^6y)^3)
20: ((8x)^-7(8x))^3
21: ((r^6s)^-2) / ((r^-5s)^3)

Or else you get totally different answers from what BigAdd has given. "


Yeh, My answers were based on that assumption.

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mamaji4
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Posted: 3rd Oct 2008 19:41 Edited at: 3rd Oct 2008 20:02
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Regarding Polynomial expansions, here is a technique that just can't go wrong.
For (x + y + z)(a + b + c)
substitute X for the first bracket, you get
X(a + b + c)
Expand this, which is easy enough
Then replace the X with its original value
In fact this method works for any expansion
X1*X2*...*Xn
as long as you take the actual contents of a SINGLE bracket at each step.

For (a + b)(c + d)
For X = (a + b)
= Xc + Xd
= (a + b)c + (a + b)d
= ac + bc + ad + bd

For Polynomial division just replace all missing powers of x in the dividend, with
0*x^n where n is the missing power of x

e.g. (12x^4 - 6x^3 + 10x) / (3x^2)

Rewrite the dividend as
12x^4 - 6x^3 + 0x^2 + 10x + 0
On division you get
4x^2 - 2x + 0 + 10/3x + 0
which reduces to the final 4x^2 - 2x + 10/3x

If there are missing powers in the divisor these too should be replaced using the same method, before doing the division, unless there is a SINGLE term in the divisor.
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Aaron Miller
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Posted: 4th Oct 2008 02:54 Edited at: 4th Oct 2008 02:54
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No that wasn't a typo - I double checked. But good news, I still passed! - What you told me helped quite a bit.

Anyways, thanks.

Cheers,

-naota

I'm not a dictator to those that do stuff for me by will. Only those who don't.
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mamaji4
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Posted: 4th Oct 2008 16:00
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Glad to be of assistance.

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Diggsey
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Posted: 4th Oct 2008 19:00 Edited at: 4th Oct 2008 19:01
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If you have more than two expressions inside the brackets, all you have to do is remember that you must multiply every one in the first brackets by every one in the second brackets:

(u+v+w)(x+y+z)

First 'u':
ux+uy+uz
Then 'v':
vx+vy+vz
Then 'w':
wx+wy+wz

Together:
ux+uy+uz+vx+vy+vz+wx+wy+wz

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