Answer :
[tex]4x\sqrt{32xv^2}+v\sqrt{2x^3}=4x\sqrt{16\cdot2}\cdot\sqrt{x}\cdot\sqrt{v^2}+v\sqrt2\cdot\sqrt{x^2\cdot x}\\\\=4x\cdot4\sqrt2\cdot\sqrt{x}\cdot v+v\sqrt2\cdot x\sqrt{x}=16xv\sqrt{2x}+xv\sqrt{2x}=17\sqrt{2x}\\\\========================================\\\\D;\\x\in < 0;\ \infty)\ \wedge\ v\in\mathbb{R}[/tex]
[tex]4x \sqrt{32xv^2}+v \sqrt{2x^3} = 4x \sqrt{16.2} . \sqrt{x} . \sqrt{v^2} + v \sqrt{2} . \sqrt{x^2} . x [/tex]
[tex]= 4x . \sqrt{2} . \sqrt{x} . v + v \sqrt{2} . x \sqrt{x} = 16 xv \sqrt{2x} + xv \sqrt{2x} [/tex] = [tex] 17\sqrt{2x} [/tex]
[tex]= 4x . \sqrt{2} . \sqrt{x} . v + v \sqrt{2} . x \sqrt{x} = 16 xv \sqrt{2x} + xv \sqrt{2x} [/tex] = [tex] 17\sqrt{2x} [/tex]
