^{2√6)}2 A.80x

^{4+8x}4√30x+24x^4 B.80x

^{6+8x}5+8x

^{5√30x+24x}4 C.104x^4 D.104x

^{4+16x}4√30

we are given

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2[/tex]

we can expand it

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x\sqrt{5x^2} +2x^2\sqrt{6} )(4x\sqrt{5x^2} +2x^2\sqrt{6} )[/tex]

we can simplify it

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x\sqrt{5}x +2x^2\sqrt{6} )(4x\sqrt{5}x +2x^2\sqrt{6} )[/tex]

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x^2\sqrt{5} +2x^2\sqrt{6} )(4x^2\sqrt{5} +2x^2\sqrt{6} )[/tex]

now, we can FOIL it

we get

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x^2\sqrt{5})^2 +2*2x^2\sqrt{6} *4x^2\sqrt{5} +(2x^2\sqrt{6} )^2[/tex]

now, we can simplify it

[tex]=4^2\cdot \:5x^4+16\sqrt{30}x^4+2^2\cdot \:6x^4[/tex]

[tex]=80x^4+16\sqrt{30}x^4+24x^4[/tex]

now, we can combine like terms

[tex]\mathrm{Add\:similar\:elements:}\:80x^4+24x^4=104x^4[/tex]

[tex]=104x^4+16\sqrt{30}x^4[/tex]

**so, option-D.............Answer**