Question

What is the following product? Assume x>0 (4x√5x^2 +2x^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

Answer 1

Answer: D

Explanation:

Answer 2

we are given

`(4x√(5x^2) +2x^2√(6) )^2`

we can expand it

`(4x√(5x^2) +2x^2√(6) )^2=(4x√(5x^2) +2x^2√(6) )(4x√(5x^2) +2x^2√(6) )`

we can simplify it

`(4x√(5x^2) +2x^2√(6) )^2=(4x√(5)x +2x^2√(6) )(4x√(5)x +2x^2√(6) )`

`(4x√(5x^2) +2x^2√(6) )^2=(4x^2√(5) +2x^2√(6) )(4x^2√(5) +2x^2√(6) )`

now, we can FOIL it

we get

`(4x√(5x^2) +2x^2√(6) )^2=(4x^2√(5))^2 +2*2x^2√(6) *4x^2√(5) +(2x^2√(6) )^2`

now, we can simplify it

`=4^2\cdot \:5x^4+16√(30)x^4+2^2\cdot \:6x^4`

`=80x^4+16√(30)x^4+24x^4`

now, we can combine like terms

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

`=104x^4+16√(30)x^4`

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