Question

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

Answer 1

`(7(2x-1)^2 (2x+5))/(2(x+3)^(1/2))`

Explanation:

Take out common factor `(2x-1)^2` and simplify,

`(2x-1)^2 {6(x+3)^(1/2) + (2x-1)/(2(x+3)^(1/2)}}`

`(2x-1)^2{(12x+36 +2x-1)/(2(x+3)^(1/2)}}`

`((2x-1)^2 (14x+35))/(2(x+3)^(1/2))`

`(7(2x-1)^2 (2x+5))/(2(x+3)^(1/2))`