Intro to calculus: differentiation (Need Help)

[stopandthink]

[math]\frac{(1+h)^2 - 1}{h} = \frac{1 + 2h + h^2 - 1}{h} = \frac{2h + h^2}{h} = \frac{h(2 + h)}{h} = 2 + h[/math]

 

I'm currently using one of the forums tutorial on calculus... And i'm stuck with a problem.

The problem is i know it works out because iv'e substituted "h" with an actual integer, and my dilemma is i can't figure out how it went from, [math]\frac{(1+h)^2 - 1}{h} = \frac{1 + 2h + h^2 - 1}{h}[/math]

 

Ignore the /font font=monospace thing, can't figure out how to remove it

Edited October 11, 2012 by stopandthink

[ewmon]

What happened to make the brackets go away?

[stopandthink]

I can't figure out how (1+h)^2 -1 = 1 + 2h+ h^2-1

 

my answer is 2+ 2h^2-1

 

Of course, my answer is incorrect but i cant see where it is i'm making a mistake.

[Axioms]

Look at how you are expanding your brackets of (1+h)^2.

It is the same as saying (1+h)(1+h)... From here you should get (1+ 2h + h^2)

 

I dont know where you are making your mistake so if you could show what you did then that could be helpful. I am pretty certain though that you are not expanding your brackets and multiplying out correctly. Remember from (1 + h)(1 + h) you must multiply every term in the first bracket by every term in the second bracket: i.e. (1*1 + 1*h + h*1 + h*h). I think this was called FOIL.. First outter inner last or something like that. If you are still struggling look up bracket expansion and how to multiply out of brackets.

 

(x+1)^3 = (x+1)(x+1)(x+1) = (x+1)(x^2+2x+1)= ((x^3)+(2x^2)+(x) + (x^2)+)(2x)+(1))

 

try expand this: (x+5)^2

[stopandthink]

Lol! i see what i did wrong,

 

Ignore this post! Thanks.

 

Look at how you are expanding your brackets of (1+h)^2.

It is the same as saying (1+h)(1+h)... From here you should get (1+ 2h + h^2)

 

I dont know where you are making your mistake so if you could show what you did then that could be helpful. I am pretty certain though that you are not expanding your brackets and multiplying out correctly. Remember from (1 + h)(1 + h) you must multiply every term in the first bracket by every term in the second bracket: i.e. (1*1 + 1*h + h*1 + h*h). I think this was called FOIL.. First outter inner last or something like that. If you are still struggling look up bracket expansion and how to multiply out of brackets.

 

(x+1)^3 = (x+1)(x+1)(x+1) = (x+1)(x^2+2x+1)= ((x^3)+(2x^2)+(x) + (x^2)+)(2x)+(1))

 

try expand this: (x+5)^2

 

Thank you! i was stuck trying to work it out some other way... Lesson learned.

[Axioms]

No problem