How do you factor $3 {(2 x - 1)}^{2} (2) {(x + 3)}^{\frac{1}{2}} + {(2 x - 1)}^{3} (\frac{1}{2}) {(x + 3)}^{- \frac{1}{2}}$ $3(2x-1)^2 (2) (x+3)^(1/2) + (2x-1)^3 (1/2) (x+3)^(-1/2)$ ?

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Answer 1 · 2015-10-09T04:56:16

$\frac{7 {(2 x - 1)}^{2} (2 x + 5)}{2 {(x + 3)}^{\frac{1}{2}}}$ $(7(2x-1)^2 (2x+5))/(2(x+3)^(1/2))$

Take out common factor ${(2 x - 1)}^{2}$ $(2x-1)^2$ and simplify,

${(2 x - 1)}^{2} {6 {(x + 3)}^{\frac{1}{2}} + \frac{2 x - 1}{2 {(x + 3)}^{\frac{1}{2}}}}$ $(2x-1)^2 {6(x+3)^(1/2) + (2x-1)/(2(x+3)^(1/2)}}$

${(2 x - 1)}^{2} {\frac{12 x + 36 + 2 x - 1}{2 {(x + 3)}^{\frac{1}{2}}}}$ $(2x-1)^2{(12x+36 +2x-1)/(2(x+3)^(1/2)}}$

$\frac{{(2 x - 1)}^{2} (14 x + 35)}{2 {(x + 3)}^{\frac{1}{2}}}$ $((2x-1)^2 (14x+35))/(2(x+3)^(1/2))$

$\frac{7 {(2 x - 1)}^{2} (2 x + 5)}{2 {(x + 3)}^{\frac{1}{2}}}$ $(7(2x-1)^2 (2x+5))/(2(x+3)^(1/2))$

How do you factor 3(2x-1)^2 (2) (x+3)^(1/2) + (2x-1)^3 (1/2) (x+3)^(-1/2)3(2x−1)2(2)(x+3)12+(2x−1)3(12)(x+3)−123(2x-1)^2 (2) (x+3)^(1/2) + (2x-1)^3 (1/2) (x+3)^(-1/2)?