24xyz² + 20x²yz - 4x²z²
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1.  We look for the largest number we can factor out of all three terms:

24, 20 and 4 can all be divided evenly by 4, so we can take out a 4
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2.  Now we look for the largest power of a letter we can factor out of
all three terms:

x occurs in all three terms. The smallest power of x is x1. So we can factor out x

y does not occur in all three terms, so we cannot take out y

z occurs in all three terms. The smallest power of z is z1. So we can factor out z.
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3.  So the GCF is their product 4xz
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4.  Start with this

4xz(

In order to get the first term 24xyz², if we were to use the 
distributive principle, the 4xz would need to be multiplied by a "6", a "y",
and a "z". So we write

4xz(6yz

In order to get the second term +20x²yz the 4xz will need to be multiplied
by a "+5", an "x", and a y. So we write

4xz(6yz + 5xy

In order to get the third term - 4x²z² the 4xz will need to be multiplied 
by a "-x", and a z. So we write

4xz(6yz + 5xy - xz

and close the parentheses:

4xz(6yz + 5xy - xz)

That's it.  Check by using the distributive principle to remove the
parentheses and you will get what you started with.

Edwin