Factor the following by taking out the greatest common factor.
9a^3b^2+81a^2b^3+108a^3b^3
the greatest common factor appears to be 9a^2b^2, so ...
To factor the expression by taking out the greatest common factor, we need to identify the common factor present in all the terms.
Looking at the coefficients (numbers), we can see that the greatest common factor of 9, 81, and 108 is 9.
Next, let's consider the variables. We have "a" appearing in all terms, and its highest power is a^3. Similarly, "b" appears in all terms, and its highest power is b^3.
Therefore, the greatest common factor of the variables is a^3b^2.
Now, we can factor out the greatest common factor:
9a^3b^2 + 81a^2b^3 + 108a^3b^3
= 9(a^3b^2) + 81(a^2b^3) + 108(a^3b^3)
Notice that all the terms are divisible by 9(a^3b^2). So, we can factor it out:
= 9(a^3b^2 + 9a^2b^3 + 12a^3b^3)
Therefore, the factored form of the expression, after taking out the greatest common factor, is:
9(a^3b^2 + 9a^2b^3 + 12a^3b^3)