Thread: can't recall algebra

Here is the problem:
step 1: k(k-1)^2 - k(k-1)
step 2: (k-1) [ k(k-1) - k]

now, the answer says the next line is this,

step 3: (k-1) [(k-1)^2 -1]

I'm confused how it goes from step 2 to step 3. There is something I've forgotten and cannot figure out how to go from step 2 to step 3. thanks.

Originally Posted by tigertina

Here is the problem:
step 1: k(k-1)^2 - k(k-1)
step 2: (k-1) [ k(k-1) - k]
now, the answer says the next line is this,
step 3: (k-1) [(k-1)^2 -1]
I'm confused how it goes from step 2 to step 3.

From k(k-1) - k to (k-1)^2 - 1 :

k(k-1) - k = k^2 - k - k = k^2 - 2k

(k-1)^2 - 1 = k^2 - 2k + 1 - 1 = k^2 - 2k

OK?