Easy basic-algebra question

[SLCentral]

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]

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

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

 

[SLCentral]

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

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 . Last step, the second sign needs to be negative. Tahnks!

 

[her209]

(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?

 

[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?

 

[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...

 

[Stunt]

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]

(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]

distribute the (x+h) throught the (x^2+2xh+h^2)

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

 

[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...

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]

damn that aint the basic algebra I remember, when did they add so many letters?

 

[SLCentral]

Originally posted by: bctbct
damn that aint the basic algebra I remember, when did they add so many letters?

Haha, this is precalc.

 

[Syringer]

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

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

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

 

[SLCentral]

bump before bed

 

[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...

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]

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...

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!

 

[probzy]

I'm not good at math. Sorry.

 

[snoopdoug1]

Originally posted by: probzy
I'm not good at math. Sorry.

thanks for the help... after the problem was solved