Question

(x-1)^7/2 - (x-1)^3/2 factor and simplify. can u explain how to do it

Answer 1

holy cow...

Answer 2

ikr

Answer 3

(x-1)^3/2((x-1)^2-1)
=(x+1)(x-1)^5/2

Answer 4

not the right answer

Answer 5

oops! calculation error!
it is
(x-1)^3/2(x-2)x

Answer 6

yes thats the right answer. my teacher gave us a packet with the problems and answers already. i just need to knw how to work it step by step.

Answer 7

can u show me how u got that

Answer 8

1 sec

Answer 9

From:
(x-1)^(7/2) - (x-1)^(3/2)

we can factor out (x-1)^(3/2), so we get:

(x-1)^(3/2) ((x-1)^2 - 1) (if you don't see why we reach this step let me know)

Then, working out the right hand portion of this we get

(x-1)^(3/2) (x^2 - 2x + 1 - 1)

The ones cancel

(x-1)^(3/2) (x^2 - 2x)

Factor out an x from the right.

(x-1)^(3/2) (x) (x - 2)

Answer 10

i get the fist step, how to factor it out. the second step i dont get how u got ((x-1)^2-1

Answer 11

Okay, we have the equation:

\[(x-1)^{\frac{7}{2}} - (x-1)^{\frac{3}{2}}\]

when we factor out the \[(x-1)^{\frac{3}{2}}\]

what we leave behind needs to be whatever you would multiply the bit we factored out by to obtain the original equation.

ie:
\[(x-1)^{\frac{3}{2}} (???) = (x-1)^{\frac{7}{2}} - (x-1)^{\frac{3}{2}}\]

okay, so we need to figure out what the ??? is.

To get the first term of the original equation, (x-1)^(7/2), what would we need to multiply (x-1)^(3/2) by?

ie..
\[(x-1)^{\frac{3}{2}} \times a = (x-1)^{\frac{7}{2}}\]
what is a?

If you have trouble seeing what a should be, think about the following:
\[x^{3} \times a = x^{7}\]
what is a here?

It should be clear that
\[a = x^{4}\]

Because when we multiply powers with like bases, we add the exponents.


so a in the first equation is:
\[a = (x-1)^{2}\]

since (3/2) + 2 = (3/2) + (4/2) = (7/2)


So we know the first part of ??? is (x-1)^2, we need another part though,
to get the -(x-1)^(3/2) from the orginal equation.

This bit is simple, since we just need to multiply our factor by -1 to get this.

So...
\[(x-1)^{\frac{3}{2}} ((x-1)^{2} - 1) = (x-1)^{\frac{7}{2}} - (x-1)^{\frac{3}{2}}\]