Prove

**Mladen1** · August 19th 2008, 09:44 AM

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.

**o_O** · August 19th 2008, 10:25 AM

$x\left[x{\color{red}(x-2)}-{\color{red}(x-2)}\right]$

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

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

We then have: $x[x{\color{red}a} - {\color{red}a}] = x[{\color{red}a}(x-1)]$

**Soroban** · August 19th 2008, 10:39 AM

Hello, Mladen1!

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

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

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 . . .

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

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