Question:
\[ 49a^2-b=(7a+\frac{1}{2})(7a-\frac{1}{2}) \]
(a) 0
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{\sqrt{2}}\)
(d) \(\frac{1}{2}\)
Solution:
\[ (7a+\frac{1}{2})(7a-\frac{1}{2}) \]
\[ =(7a)^2-(\frac{1}{2})^2 \]
\[ =49a^2-\frac{1}{4} \]
\[ 49a^2-b=49a^2-\frac{1}{4} \]
\[ b=\frac{1}{4} \]
\[ \boxed{\frac{1}{4}} \]