Question

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

Answer 1

Welcome to OpenStudy!

Happy to help you with this problem. There is, however, some ambiguity here, and so I'm hoping I can convince you to present the problem again, either with a shared screen shot or by drawing it within the Draw utility.

That 2a^x is perfectly clear. But by 1/2b^x, do you mean (1/2) / b^x? or 1 / (2b^x)?

Answer 2

Thank you for sharing this screen shot. This image clearly shows that that 1/2 MUST be enclosed within parentheses, and that that b^x goes into the numerator.

\[(2a^x+\frac{ 1 }{ 2 }b^x)^2\]has the form \[(x+y)^2\]...which is the square of the binomial (x+y). Do you recall what the expanded version of \[(x+y)^2 \]...is?

If so, use that pattern to expand \[(2a^x+\frac{ 1 }{ 2 }b^x)^2\]