Respuesta :
Answer:
The product of the given expression is
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2=104x^4+16\sqrt{30}x^4[/tex]
or
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2=(104+16\sqrt{30})x^4[/tex]
Step-by-step explanation:
Given that the expression is
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2[/tex]
Assume that x>0
To find the product of the given expression:
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2[/tex]
We may write it as
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2=(4x\sqrt{5x^2}+2x^2\sqrt{6})\times (4x\sqrt{5x^2}+2x^2\sqrt{6})[/tex]
Now using the distributive property (each term in the expression is multiplied to each term in the another expression
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2=(4x\sqrt{5}x+2x^2\sqrt{6})\times (4x\sqrt{5}x+2x^2\sqrt{6})[/tex]
[tex]=(4x^2\sqrt{5}+2x^2\sqrt{6})\times (4x^2\sqrt{5}+2x^2\sqrt{6})[/tex]
[tex]=(4x^2\sqrt{5})(4x^2\sqrt{5})+(4x^2\sqrt{5})(2x^2\sqrt{6})+(2x^2\sqrt{6})(4x^2\sqrt{5})+(2x^2\sqrt{6})(2x^2\sqrt{6})[/tex]
[tex]=(4x^2\sqrt{5})^2+8x^4\sqrt{5}\sqrt{6}+8x^4\sqrt{6}\sqrt{5}+4x^4(6)[/tex]
[tex]=16x^4(5)+16x^4\sqrt{5}\sqrt{6}+24x^4[/tex]
[tex]=80x^4+16x^4\sqrt{5\times6}+24x^4[/tex]
[tex]=80x^4+16x^4\sqrt{30}+24x^4[/tex]
[tex]=80x^4+16\sqrt{30}x^4+24x^4[/tex]
Adding the like terms
[tex]=104x^4+16\sqrt{30}x^4[/tex]
Therefore
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2=104x^4+16\sqrt{30}x^4[/tex]
Therefore the product of the given expression is
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2=104x^4+16\sqrt{30}x^4[/tex]
or
[tex](4x\sqrt{5x^2}+2x^2\sqrt{6})^2=(104+16\sqrt{30})x^4[/tex]
Answer:
D on edge is correct ;-;
Step-by-step explanation:
brainliest plz :)
