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
