Ok sooo it starts with (x+h)*3 - 2 - (x*3 - 2)
Then you cube the (x+h), right, and that ends up being
hx*3 + 2h*2x*2 = h*3x - 2 - x*3 + 2
So the twos cancel out and it's just
hx*3 + 2h*2x*2 = h*3x - x*3
right?
Oh yeah and this has all been over h
So the book has the answer as 3x*2 + 3xh + h*2
But I have no idea how...
Help?
Answers:
Then you cube the (x+h), right, and that ends up being
hx*3 + 2h*2x*2 = h*3x - 2 - x*3 + 2 (the cubing is incorrect...)
------------------------------...
Here's how you do the cube... (^ means raise to the power)
(x+h)^3 = (x+h)(x+h)(x+h). right? OR (x+h)^3 = (x+h)^2 (x+h)
What is (x+h)(x+h)? (x+h)(x+h) = x^2 + 2xh + h^2
Sooo...
(x+h)^3 = (x+h)^2 (x+h) = (x^2 + 2xh + h^2)(x+h)
** pretend the (x^2 + 2xh + h^2) is a whole number. distribute like you would a whole number to the terms in the ( )'s **
= (x^2 + 2xh + h^2)(x) + (x^2 + 2xh + h^2)(h)
** now distribute the "x" to each of the terms in the ()'s in front of the (x)... and distribute the "h" to each of the terms in the ()'s in front of the (h)... ** ... you should get...
= x^3 + 2hx^2 + xh^2 + hx^2 + 2xh^2 + h^3
** combine "like" terms... **
= x^3 + 3hx^2 + 3xh^2 + h^3 (This is what you should get for the cube)
Okay... back to your problem... and substitute what we found for (x+h)^3...
(x+h)^3 - 2 - (x^3 - 2)
= x^3 + 3hx^2 + 3xh^2 + h^3 - 2 - x^3 + 2...
** yes... the 2's cancel out. so do the x^3 's **
= 3hx^2 + 3xh^2 + h^3
And you said that this is all over "h"...
okay...
3hx^2 + 3xh^2 + h^3
---------------------------- = 3x^2 + 3xh + h^2
..... h
BTW, ^ means raised to the power of, * means multiply...
(x+h)^3 = (x+h)(x+h)(x+h),
. so using the FOIL method for (x+h)(x+h) first...
x*x + x*h + h*x + h*h = x^2 + 2xh + h^2
so then you have to take this and multiply it by (x+h) which gives you.
(x+h)(x^2+2xh+h^2)
= x*x^2 + x*2xh + x*h^2 + h*x^2 + h*2xh + h*h^2
= x^3 + 2x^2h + x^2h+ xh^2 + 2xh^2 + h^3
= x^3 + 3x^2h + 3xh^2 + h^3
so your problem becomes: (all over h)
x^3 + 3x^2h + 3xh^2 + h^3 - 2 - (x^3 - 2) =
=x^3 + 3x^2h + 3xh^2 + h^3 + -2 + -x^3 + 2 =
.. the -2 cancels 2
=x^3 + 3x^2h + 3xh^2 + h^3 + -x^3
. the -x^3 cancels x^3
= 3x^2h + 3xh^2 + h^3 (divided by h)
because the entire thing is over h, divide one h out of each term. 3x^2h/h = 3x^2 3xh^2/h = 3xh h^3/h = h^2
= 3x^2 + 3xh + h^2
your mistake was in calculating (x+h)^3
(x+h)^3 does NOT equal x^3 + h^3...try substituting two different numbers in for x and h and you'll see...(4+5)^3 = 729 4^3 + 5^3 doesn't even come close...
Good work, other than that! Rewrite these numbers 'normally' (man I wish it would work on this site!) and it is easier to follow. feel free to ask again!
This article contents is post by this website user, EduQnA.com doesn't promise its accuracy.
More Questions & Answers...