Expanding and then simplifying

**scotchegg** · May 5th 2010, 01:54 PM

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.

**Anonymous1** · May 5th 2010, 01:59 PM

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.

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

**scotchegg** · May 5th 2010, 02:13 PM

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?

**pickslides** · May 5th 2010, 02:18 PM

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.

**Anonymous1** · May 5th 2010, 03:03 PM

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.

**GuMing** · May 5th 2010, 11:15 PM

is the final answer

**scotchegg** · May 6th 2010, 09:08 AM

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...

**Anonymous1** · May 6th 2010, 09:27 AM

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.

**scotchegg** · May 6th 2010, 09:29 AM

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...

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