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What is the following product? Assume x>0 (4x√5x^2 +2x2√6)2 A.80x4+8x4√30x+24x^4 B.80x6+8x5+8x5√30x+24x4 C.104x^4 D.104x4+16x4√30
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Best Answer

we are given

$$(4x\sqrt{5x^2} +2x^2\sqrt{6} )^2$$

we can expand it

$$(4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x\sqrt{5x^2} +2x^2\sqrt{6} )(4x\sqrt{5x^2} +2x^2\sqrt{6} )$$

we can simplify it

$$(4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x\sqrt{5}x +2x^2\sqrt{6} )(4x\sqrt{5}x +2x^2\sqrt{6} )$$

$$(4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x^2\sqrt{5} +2x^2\sqrt{6} )(4x^2\sqrt{5} +2x^2\sqrt{6} )$$

now, we can FOIL it

we get

$$(4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x^2\sqrt{5})^2 +2*2x^2\sqrt{6} *4x^2\sqrt{5} +(2x^2\sqrt{6} )^2$$

now, we can simplify it

$$=4^2\cdot \:5x^4+16\sqrt{30}x^4+2^2\cdot \:6x^4$$

$$=80x^4+16\sqrt{30}x^4+24x^4$$

now, we can combine like terms

$$\mathrm{Add\:similar\:elements:}\:80x^4+24x^4=104x^4$$

$$=104x^4+16\sqrt{30}x^4$$

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

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