Factorizing

Question

How to make factors of following

 

 

a²-2ax+x²-4b²

 

 

 

9a²-c²-4cx+4x²

Answer 1

Factor by grouping:

 

a²-2ax+x²-4b² = (a²-2ax+x²) - (4b²) = (a-x)² - (2b)²

 

                                                  = (a-x+2b)(a-x-2b)

 

I don't think that 9a²-c²-4cx+4x² is factorable.  However, if there is a typo and "+4x² " is changed to "-4x² ", then:

 

9a²-c²-4cx-4x² = (9a²) - (c²+4cx+4x²)

 

                     = (3a)² - (c+2x)²

 

                     = (3a-(c+2x))(3a+(c+2x))

 

                     = (3a-c-2x)(3a+c+2x)