Question

How do you factor `(x-3)^2(2x+1)^3+(x-3)^3(2x+1)^2`?

Answer 1

`(x-3)^2(2x+1)^3+(x-3)^3(2x+1)^2=(x-3)^2(2x+1)^2(3x-2)`

Explanation:

Both of the two expressions are divisible by `(x-3)^2(2x+1)^2`, so separate that out, then resolve the remaining terms:

`(x-3)^2(2x+1)^3+(x-3)^3(2x+1)^2`

`=(x-3)^2(2x+1)^2((2x+1)+(x-3))`

`=(x-3)^2(2x+1)^2(3x-2)`