The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

Question

Quizplus · Accepted Answer

We can factor by grouping: 
$64a^3b^3 - 16a^2b^4 + 8a^2b^2 = 8a^2b^2(8ab-2b^2+1)$
Then we can divide out the common factor of $8a^2b^2$ from the numerator and denominator: 
$\frac{64a^3b^3}{8a^2b^2} = 8ab$
$\frac{-16a^2b^4}{8a^2b^2} = -2b^2$
$\frac{8a^2b^2}{8a^2b^2} = 1$
So the final answer is $\frac{8ab-2b^2+1}{1} = 8ab-2b^2+1$. 
Therefore, the correct choice is (B).

The Following Problem Involves Some Factoring by Grouping