Answer :
The greatest common factor (GCF) of the given expression 36x^9y^9 + 60x^5y^6 - 120x^7y^2 is 12x^5y^2. Factoring out the GCF simplifies the expression to 12x^5y^2(3x^4y^7 + 5y^4 - 10x^2).
To factor out the greatest common factor (GCF), we look for the highest power of each variable (x and y) that appears in all terms. In this case, the highest power of x that appears in all terms is x^5, and the highest power of y that appears in all terms is y^2.
We then divide each term by the GCF, which is 12x^5y^2. Dividing the expression by the GCF yields:
36x^9y^9 / (12x^5y^2) + 60x^5y^6 / (12x^5y^2) - 120x^7y^2 / (12x^5y^2)
Simplifying each term, we get:
3x^4y^7 + 5y^4 - 10x^2
Therefore, the factored form of the expression 36x^9y^9 + 60x^5y^6 - 120x^7y^2 is 12x^5y^2(3x^4y^7 + 5y^4 - 10x^2).
Learn more about factoring and simplifying expressions here: brainly.com/question/29144651
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