i need help with special factorization. the problem is (x-3)^2(2x+1)^3+(x-3)^3(2x-1)^2 when i put it into a problem solving website, they gave me the answer (x-3)^2(2x+1)^2(3x-2), but i dont understand where they got that from.

Question

anonymous · Answer

does anyone know the steps to solve it?

anonymous · Answer

(x-3)^2(2x+1)^3 + (x-3)^3(2x-1)^2 
take out the common factors...
(x-3)^2(2x+1)^2 * [(2x+1) + (x-3)]

anonymous · Answer

first you can take out (x-3)^2 to give
(x-3)^2[(2x+1)^3 + (x-3)(2x-1)^2]

anonymous · Answer

(x-3)^2(2x+1)^2 * [(2x+1) + (x-3)]
this further gives
(x-3)^2(2x+1)^2 * [2x+1 + x-3]
finally u get
(x-3)^2(2x+1)^2 * [3x -2]


i hope it is clear now.......

anonymous · Answer

yes that helps a lot! thank you!

anonymous · Answer

got a medal for me  ??.....☺