Bài 1. Làm tính chia:
a)\(\left( { – 4{a^5}{b^2} – {4 \over 9}{a^4}{b^5} + {2 \over 3}{a^3}{b^6}} \right):\left( {{2 \over 3}{a^3}{b^2}} \right)\)
b)\(\left( {9{x^3}{y^2} – 3{x^2}{y^3} + {x^2}{y^2}} \right):\left( {3{x^2}{y^2}} \right).\)
Bài 2. Rút gọn biểu thức:
a)\(\left( {3{x^2} – 2{x^2}y} \right):{x^2} – \left( {2x{y^2} + {x^2}y} \right):\left( {{1 \over 3}xy} \right)\)
b) \(5{x^3}:x – {\left( {2x} \right)^2} + {x^4}:\left( {2{x^2}} \right).\)
Bài 3. Tính giá trị của biểu thức:
\(\left( {8{x^3} – 4{x^2}} \right):\left( {2{x^2}} \right) – \left( {4{x^2} – 3x} \right):x + 2x,\) với \(x = – 1.\)
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Bài 1. a) \(\left( { – 4{a^5}{b^2} – {4 \over 9}{a^4}{b^5} + {2 \over 3}{a^3}{b^6}} \right):\left( {{2 \over 3}{a^3}{b^2}} \right)\)
\(=\left( { – 4{a^5}{b^2}:{2 \over 3}{a^3}{b^2}} \right) + \left( { – {4 \over 9}{a^4}{b^5}:{2 \over 3}{a^3}{b^2}} \right) + \left( {{2 \over 3}{a^3}{b^6}:{2 \over 3}{a^3}{b^2}} \right)\)
\(= – 6{a^2} – {2 \over 3}a{b^3} + {b^4}.\)
b) \(\left( {9{x^3}{y^2} – 3{x^2}{y^3} + {x^2}{y^2}} \right):\left( {3{x^2}{y^2}} \right)\)
\(=\left( {9{x^3}{y^2}:3{x^2}{y^2}} \right) + \left( { – 3{x^2}{y^3}:3{x^2}{y^2}} \right) + \left( {{x^2}{y^2}:3{x^2}{y^2}} \right) \)
\(= 3x – y + {1 \over 3}.\)
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Bài 2. a) \(\left( {3{x^2} – 2{x^2}y} \right):{x^2} – \left( {2x{y^2} + {x^2}y} \right):\left( {{1 \over 3}xy} \right)\)
\(=\left( {3{x^3}:{x^2}} \right) + \left( { – 2{x^2}y:{x^2}} \right) \)\(\;- \left[ {\left( {2x{y^2}:{1 \over 3}xy} \right) + \left( {{x^2}y:{1 \over 3}xy} \right)} \right]\)
\(=3x – 2y – \left( {6y + 3x} \right) \)
\(= 3x – 2y – 6y – 3x = – 8y.\)
b) \(5{x^3}:x – {\left( {2x} \right)^2} + {x^4}:\left( {2{x^2}} \right)\)
\(\; = 5{x^2} – 4{x^2} + {1 \over 2}{x^2} = {3 \over 2}{x^2}.\)
Bài 3. \(\left( {8{x^3} – 4{x^2}} \right):\left( {2{x^2}} \right) – \left( {4{x^2} – 3x} \right):x + 2x\)
\(=4x – 2 – \left( {4x – 3} \right) + 2x \)
\(= 4x – 2 – 4x + 3 + 2x = 2x + 1\)
Thay \(x = – 1,\) ta được: \(2.( – 1) + 1 = – 1.\)
