SOLUTION: Which of the following is equivalent to the expression 16x^8-100y^6 ? A. (8x^4+50y^3)(8x^4-50y^3) B. (8x^4+50y^4)(8x^4-50y^2) C. (4x^4+10y^3)(4x^4-10y^3) D. (4x^4+10y^4)(4x^4-1

FOIL them all out and see:

A.  NO
B.  NO
C.  NO
D.  YES

Even though D is the correct answer, it's not completely factored.
If fact D, although mathematically correct, is not what you should 
do first when factoring.

Here's the correct way to do the problem:



Factor out greatest common factor of 4. That's what you should do first,
always!



Write  as  and  as 

 

Factor the difference of squares.



That's the correct complete factorization even though 
it is not listed.

Edwin