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

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Answer 1 · 2017-02-07T21:39:10

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

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

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

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

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

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