Factorising

**mikey18** · May 16th 2008, 06:21 AM

Can someone please help me.

36x^2z-6xyz-6y^2z?

**TheEmptySet** · May 16th 2008, 06:53 AM

Originally Posted by mikey18

Can someone please help me.

36x^2z-6xyz-6y^2z?

I think you mean this

$36x^2z-6xyz-6y^2z$

Now come the "trick"
lets add zero to the equation $0=(12xyz-12xyz)$

$36x^2z-6xyz-6y^2z+0 \to 36x^2z-6xyz-6y^2z+12xyz-12xyz$

Now rewriting as

$36x^2z-18xyz+12xyz-6y^2z \iff 18xz(2x-y)+6yz(2x-y)$

$(2x-y)(18xz+6yz)=6(2x-y)(3xz+yz)$

**Soroban** · May 16th 2008, 07:03 AM

Hello, mikey18!

Factor: . $36x^2z-6xyz-6y^2z$

Factor out the common factor $6z\!:\quad 6z(6x^2 - xy - y^2)$

Then factor the trinomial: . $6z(2x - y )(3x + y )$

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