Easy basic-algebra question

SLCentral

Diamond Member
Feb 13, 2003
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0
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Working on some precalc work right now, and last years math class seems to have lost my mind.

When doing:
(x+h)^3

Would I do:
(x^2+2xh+h^2)(x+h)

Then:

X^3 + 3h^2x + 3hx^2 + h^3

What am I missing here? Anything?

Thanks!
 

schneiderguy

Lifer
Jun 26, 2006
10,801
91
91
Originally posted by: SLCentral

Would I do:
(x^2+2xh+h^2)(x+h)

i think one of those +'s needs to turn into a minus sign.im just not sure which one :p

then again, i could and probably am completely wrong :Q

 

SLCentral

Diamond Member
Feb 13, 2003
3,542
0
71
Originally posted by: schneiderguy
Originally posted by: SLCentral

Would I do:
(x^2+2xh+h^2)(x+h)

i think one of those +'s needs to turn into a minus sign.im just not sure which one :p

then again, i could and probably am completely wrong :Q

That's what I'm thinking. I remember being taught MOP, which is Match, Opposite, Positive. But I can't remember where I do that!

EDIT: Remembered where it goes :p. Last step, the second sign needs to be negative. Tahnks!
 

her209

No Lifer
Oct 11, 2000
56,336
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0
(x+h)(x+h)(x+h) = (x^2+2xh+h^2)(x+h) = x^3+2hx^2+xh^2+hx^2+2xh^2+h^3 = x^3+3hx^2+3xh^2+h^3

Remember Pascal's Triangle?
 

Stunt

Diamond Member
Jul 17, 2002
9,717
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(x+h)(x+h)(x+h) = (x^2+2xh+h^2)(x+h)
(x^2+2xh+h^2)(x+h) = x^3 + 3x^2h + 3xh^2 + h^3

Yeah you got it...:p
 

Stunt

Diamond Member
Jul 17, 2002
9,717
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Originally posted by: SLCentral
Originally posted by: her209
(x+h)(x+h)(x+h) = (x^2+2xh+h^2)(x+h)

Yeah, my big problem is that step right there. What should I do exactly after that?
Multiply each term using distributive law. :)

ie. x^2*x + x^2*h + 2xh*x +2xh*h + h^2*x +h^2*h
 

RapidSnail

Diamond Member
Apr 28, 2006
4,257
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(x + h)^3

(x + h)(x + h)(x + h)

(x^2 + 2xh + h^2)(x + h)

(x^2 + 2xh + h^2)x + (x^2 + 2xh + h^2)h

(x^3 + 2x^2h + xh^2) + (x^2h + 2xh^2 + h^3)

x^3 + 3x^2h + 3xh^2 + h^3



No, you're not missing anything.
 

bobert

Senior member
Dec 6, 2004
505
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distribute the (x+h) throught the (x^2+2xh+h^2)

x^3 + 3(x^2)h + 3x(h^2) + h^3
 

SLCentral

Diamond Member
Feb 13, 2003
3,542
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Originally posted by: Stunt
(x+h)(x+h)(x+h) = (x^2+2xh+h^2)(x+h)
(x^2+2xh+h^2)(x+h) = x^3 + 3x^2h + 3xh^2 + h^3

Yeah you got it...:p

Sweet, that's what I'm getting. But now why am I not getting the right answer? I'm evaluating a difference quotiant, so throw that over h, and I should be getting 3x^2 +1.

Original problem: f(x) = x^3 + x

What I need to simplify:

(x+h)^3 + (x+h) -(x^3+x)
--------------------------------
h

So...

x^3 + 3x^2h + 3xh^2 + h^3 + x + h - x^3 -x
---------------------------------
h

Turns into...

3x^2h + 3xh^2 + h^3 + h
--------------------------------
h

Considering h=0, and is just used for simplifying, and the simplified answer SHOULD be 3x^2 + 1, what do I do next?

The only thing I see is to pull out the h:

h(3x^2 + 3xh + h^2 + 1)

But that leaves me with a unnecessary 3xh. What am I missing here?
 

bctbct

Diamond Member
Dec 22, 2005
4,868
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damn that aint the basic algebra I remember, when did they add so many letters? :D
 

Syringer

Lifer
Aug 2, 2001
19,333
2
71
Originally posted by: schneiderguy
Originally posted by: SLCentral

Would I do:
(x^2+2xh+h^2)(x+h)

i think one of those +'s needs to turn into a minus sign.im just not sure which one :p

then again, i could and probably am completely wrong :Q

They're all plusses, where would a minus come from? :confused:
 

brikis98

Diamond Member
Jul 5, 2005
7,253
8
0
Originally posted by: SLCentral
Originally posted by: Stunt
(x+h)(x+h)(x+h) = (x^2+2xh+h^2)(x+h)
(x^2+2xh+h^2)(x+h) = x^3 + 3x^2h + 3xh^2 + h^3

Yeah you got it...:p

Sweet, that's what I'm getting. But now why am I not getting the right answer? I'm evaluating a difference quotiant, so throw that over h, and I should be getting 3x^2 +1.

Original problem: f(x) = x^3 + x

What I need to simplify:

(x+h)^3 + (x+h) -(x^3+x)
--------------------------------
h

So...

x^3 + 3x^2h + 3xh^2 + h^3 + x + h - x^3 -x
---------------------------------
h

Turns into...

3x^2h + 3xh^2 + h^3 + h
--------------------------------
h

Considering h=0, and is just used for simplifying, and the simplified answer SHOULD be 3x^2 + 1, what do I do next?

The only thing I see is to pull out the h:

h(3x^2 + 3xh + h^2 + 1)

But that leaves me with a unnecessary 3xh. What am I missing here?

a difference quotient is

lim h -> 0 [f(x+h) - f(x)] / h

so the numerator becomes

[(x+h)^3 + x + h] - x^3 - x

x^3 + 3hx^2 + 3xh^2 + h^3 + x + h - x^3 - x

3hx^2 + 3xh^2 + h^3 + h

h(3x^2 + 3xh + h^2 + 1)

dividing the numerator by the denominator cancels the h and we get:

lim h -> 0 3x^2 + 3xh + h^2 + 1 = 3x^2 + 1

which, as you'll learn, is precisely the derivative of f(x).
 

SLCentral

Diamond Member
Feb 13, 2003
3,542
0
71
Originally posted by: brikis98
Originally posted by: SLCentral
Originally posted by: Stunt
(x+h)(x+h)(x+h) = (x^2+2xh+h^2)(x+h)
(x^2+2xh+h^2)(x+h) = x^3 + 3x^2h + 3xh^2 + h^3

Yeah you got it...:p

Sweet, that's what I'm getting. But now why am I not getting the right answer? I'm evaluating a difference quotiant, so throw that over h, and I should be getting 3x^2 +1.

Original problem: f(x) = x^3 + x

What I need to simplify:

(x+h)^3 + (x+h) -(x^3+x)
--------------------------------
h

So...

x^3 + 3x^2h + 3xh^2 + h^3 + x + h - x^3 -x
---------------------------------
h

Turns into...

3x^2h + 3xh^2 + h^3 + h
--------------------------------
h

Considering h=0, and is just used for simplifying, and the simplified answer SHOULD be 3x^2 + 1, what do I do next?

The only thing I see is to pull out the h:

h(3x^2 + 3xh + h^2 + 1)

But that leaves me with a unnecessary 3xh. What am I missing here?

a difference quotient is

lim h -> 0 [f(x+h) - f(x)] / h

so the numerator becomes

[(x+h)^3 + x + h] - x^3 - x

x^3 + 3hx^2 + 3xh^2 + h^3 + x + h - x^3 - x

3hx^2 + 3xh^2 + h^3 + h

h(3x^2 + 3xh + h^2 + 1)

dividing the numerator by the denominator cancels the h and we get:

lim h -> 0 3x^2 + 3xh + h^2 + 1 = 3x^2 + 1

which, as you'll learn, is precisely the derivative of f(x).

So the entire time I was doing it correctly? Wow, I feel dumb. Luckily, my teacher taught us how to get the derivative using the exponents (times exponent by coefficient, etc.) so it's pretty hard for me to get the wrong answer on the quiz today :).

Thanks everyone!