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Home Q & A Board Science-Related Homework Help Mathematics
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leonardyi leonardyi
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11 years ago
How do you factor out the greatest common factor?

16x^9y^9 - 24x^6y^7 - 16x^3y^2

How would you do a problem like this or factoring it out? I dont understand please help me understand how you would factor out the greatest common factor.

Please&thank you!
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Firedancer20Firedancer20
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11 years ago
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11 years ago
nikki--

First look at the factored form of each term:

16x^9y^9 =
2 * 2 * 2 * 2 * x * x * x * x * x * x * x * x * x * y * y * y * y * y * y * y * y * y.

24x^6y^7 =
2 * 2 * 2 * 3 * x * x * x * x * x * x * y * y * y * y * y * y * y.

16x^3y^2 =
2 * 2 * 2 * 2 * x * x * x * y * y.

Now count the factors that show up in all three terms.  Each of them have three factors of 2, three factors of x and two factors of y.  We don't use 3 because that isn't a factor of all three terms.

2 * 2 * 2 * x * x * x * y * y is the greatest common factor or 8x^3y^2.  Now the fun stuff begins.  If we take the GCF out of each of the original numbers(go back and cross out ee factors of 2, three factors of x and two factors of y in each term) we get:


8x^3y^2(2x^6y^7 - 3x^3y^5 - 2).  Simplest form.
 
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