How do you factor (2x+3)^2(x-5)^2+(2x+3)(x-5)^3 using GCF.

I think the answer is (x-5)^2(2x+3)(3x-2) but I dnt know how to get it.

Start: (2x+3)^(2)(x-5)^(2)+(2x+3)(x-5)^(3)

Factor out the GCF of (2x+3)(x-5)^(2) from each term in the polynomial.
(2x+3)(x-5)^(2)((2x+3))+(2x+3)(x-5)^(2)…

Factor out the GCF of (2x+3)(x-5)^(2) from (2x+3)^(2)(x-5)^(2)+(2x+3)(x-5)^(3).
(2x+3)(x-5)^(2)((2x+3)+(x-5))

Remove the parentheses that are not needed from the expression.
(2x+3)(x-5)^(2)(2x+3+x-5)

Since 2x and x are like terms, add x to 2x to get 3x.
(2x+3)(x-5)^(2)(3x+3-5)

Subtract 5 from 3 to get -2.
(2x+3)(x-5)^(2)(3x-2)

(2x+3)^2(x-5)^2+(2x+3)(x-5)^3

=(2x+3)(2x+3)(x-5)(x-5)+(2x+3)(x-5)(x-…

tracing common factor


=(2x+3)(x-5)(x-5)[(2x+3) +(x--5)]

=(x-5)^2(2x+3)[2x+3+x-5]

=(x--5)^2(2x+3)[3x --2]

(x - 5)^2 (2x + 3)[2x + 3 + x - 5]
= (x - 5)^2 (2x + 3)(3x - 2)