Answer:
[tex](4a^{2x} )+2a^{x} b^{x} + \frac{b^{2x} }{4}[/tex]
Step-by-step explanation:
The given equation is
[tex](2a^x + \frac{1}{2}b^{x} } )^2[/tex] ...........(i)
we know the formula i.e.
[tex](a+b)^{2}= a^{2}+ b^{2} +2(a)(b)[/tex]
Applying this formula on equation (i) gives
= [tex](2a^{x} )^{2} +(\frac{1}{2})^{2}*(b^{x} )^{2} + 2 (2a^{x} )(\frac{1}{2} b^{x})[/tex]
Opening the sqaure gives and canceling [tex]\frac{1}{2}[/tex] with 2 gives us
= [tex]4a^{2x} + \frac{1}{4}b^{2x} + 2a^{x}b^{x}[/tex]
= [tex](4a^{2x} )+2a^{x} b^{x} + \frac{b^{2x} }{4}[/tex]
which is the answer
