Rút gọn \(\frac{{ - 3\sqrt {16a} + 5a\sqrt {16a{b^2}} }}{{2\sqrt a }}\) (với a > 0, b > 0).
Giải thích
\(\frac{{ - 3\sqrt {16a} + 5a\sqrt {16a{b^2}} }}{{2\sqrt a }} = \frac{{ - 3\sqrt {16a} }}{{2\sqrt a }} + \frac{{5a\sqrt {16a{b^2}} }}{{2\sqrt a }}\)
\( = \frac{{ - 3}}{2}\sqrt {\frac{{16a}}{a}} + \frac{{5a}}{2} \cdot \sqrt {\frac{{16a{b^2}}}{a}} \)\( = \frac{{ - 3}}{2}\sqrt {16} + \frac{{5a}}{2}.\sqrt {16{b^2}} \)
\( = \frac{{ - 3}}{2}.4 + \frac{{5a}}{2}.4b\)\( = - 6 + 10ab.\)