# Prove

• Aug 19th 2008, 09:44 AM
Prove
Hello

I need to prove this and im having som trouble doing it.

x(x(x-2)-(x-2)) = x(x-2)(x-1)

Thank you for any assistance.
• Aug 19th 2008, 10:25 AM
o_O
$\displaystyle x\left[x{\color{red}(x-2)}-{\color{red}(x-2)}\right]$

Focus on the inside expression. Factor the red out to get your desired answer.

If it helps, imagine $\displaystyle a = {\color{red}(x-2)}$.

We then have: $\displaystyle x[x{\color{red}a} - {\color{red}a}] = x[{\color{red}a}(x-1)]$
• Aug 19th 2008, 10:39 AM
Soroban

Quote:

I need to prove this and I'm having some trouble doing it.

. . $\displaystyle x[x(x-2)-(x-2)] \:= \:x(x-2)(x-1)$

Exactly what is stopping you?

[1] Multiply out both sides and show that they are equal! . . . Duh!

[2] Or we can factor the left side . . .

. . $\displaystyle x\bigg[x\underbrace{(x-2)} - \underbrace{(x-2)}\bigg]$
. . . . .
common factor
. . . . . . .$\displaystyle \downarrow$ . .$\displaystyle \swarrow$
. .$\displaystyle = \quad\;\; x(x-2)(x-1)$