# Math Help - Expanding and then simplifying

1. ## Expanding and then simplifying

Basically the question was in an exam I sat today, and it states

Expand Fully and simplify:

$x(x-1)^2$

Basically everyone has a different answer, and so I was wondering if any of you could help me out? Thanks.

2. Originally Posted by scotchegg
Basically the question was in an exam I sat today, and it states

Expand Fully and simplify:

x(x-1)^2

Basically everyone has a different answer, and so I was wondering if any of you could help me out? Thanks.
$x(x-1)^2 = x(x-1)(x-1) = x(x^2 -2x +1) = x^3 -2x^2 +x.$

3. Originally Posted by Anonymous1
$x(x-1)^2 = x(x-1)(x-1) = x(x^2 -2x +1) = x^3 -2x^2 +x.$
But then it says to simplify? which is where everything falls apart... We got to the
$x^3 -2x^2 +x$
although can you simplify that?

Or am I reading into the question too much?

4. Originally Posted by scotchegg
$x^3 -2x^2 +x$
although can you simplify that?
There are no like terms here, therefore you cannot simplify it any further.

5. I think your teachers thought process was...

$x(x-1)^2$

$= x(x-1)(x-1)$ expanded

$= x(x^2 -2x +1)$ fully expanded

$= x^3 -2x^2 +x$ simplified

...Which is poorly worded, but I'm going to go out on a limb and guess he wasn't an english major.

6. is the final answer

7. One of my friends got the answer

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

Trying to convince him that it is wrong, but im not sure...
Plus the teacher wont give us the test back until at least next Friday as we were the first class to sit the test...

8. Originally Posted by scotchegg
One of my friends got the answer

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

Trying to convince him that it is wrong, but im not sure...
Plus the teacher wont give us the test back until at least next Friday as we were the first class to sit the test...

Yes,

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

It's going to come down to semantics. I don't know why your teacher would say "simplify" when he meant "factor," though.

9. Originally Posted by Anonymous1
Yes,

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

It's going to come down to semantics. I don't know why your teacher would say "simplify" when he meant "factor," though.
Our teachers never make up good tests, so this one will probably be a very awkward question for them!

Thanks to everyone that contributed, roll on results day...