Respuesta :
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
