Rút gọn biểu thức sau: \( \sqrt {{{\left( {a - b} \right)}^2}} - 3\sqrt {{a^2}} + 2\sqrt {{b^2}} \)

* Hướng dẫn giải

 \( \sqrt {{{\left( {a - b} \right)}^2}} - 3\sqrt {{a^2}} + 2\sqrt {{b^2}} = \left| {a - b} \right| - 3\left| a \right| + 2\left| b \right|\)

Vì 

\(\begin{array}{l} a < 0 < b \to \left\{ \begin{array}{l} a - b < 0\\ a < 0\\ b > 0 \end{array} \right. \to \left\{ \begin{array}{l} \left| {a - b} \right| = b - z\\ \left| a \right| = - a\\ \left| b \right| = b \end{array} \right.\\ \begin{array}{*{20}{l}} { \Rightarrow \left| {a - b} \right| - 3\left| a \right| + 2\left| b \right| = b - a - 3\left( { - a} \right) + 2b}\\ { = b - a + 3a + 2b}\\ { = b - a + 3a + 2b}\\ { = 2a + 3b.} \end{array} \end{array}\)