Question

Solve (2a^x + 1/2b^x)^2

Answer 1

Answer:

$(4a^{2x} )+2a^{x} b^{x} + \frac{b^{2x} }{4}$

Step-by-step explanation:

The given equation is

$(2a^x + \frac{1}{2}b^{x} } )^2$ ...........(i)

we know the formula i.e.

$(a+b)^{2}= a^{2}+ b^{2} +2(a)(b)$

Applying this formula on equation (i) gives

= $(2a^{x} )^{2} +(\frac{1}{2})^{2}*(b^{x} )^{2} + 2 (2a^{x} )(\frac{1}{2} b^{x})$

Opening the sqaure gives and canceling  $\frac{1}{2}$ with 2 gives us

= $4a^{2x} + \frac{1}{4}b^{2x} + 2a^{x}b^{x}$

= $(4a^{2x} )+2a^{x} b^{x} + \frac{b^{2x} }{4}$

which is the answer