Thu gọn các đa thức sau: (a) (30x^4y^3−2/5x^2y^3−3x^4y^4):(5x^2y^3).

a) \(\left( {30{x^4}{y^3} - 25{x^2}{y^3} - 3{x^4}{y^4}} \right):\left( {5{x^2}{y^3}} \right)\)

\( = \left( {30{x^4}{y^3}} \right):\left( {5{x^2}{y^3}} \right) - \left( {25{x^2}{y^3}} \right):\left( {5{x^2}{y^3}} \right) - \left( {3{x^4}{y^4}} \right):\left( {5{x^2}{y^3}} \right)\)

\( = 6{x^2} - 5 - \frac{3}{5}{x^2}y\)

\( = - \frac{3}{5}{x^2}y + 6{x^2} - 5\)

b) \({x^3}{y^4} \cdot \left( {{x^2} - 2{y^3}} \right) - 2{x^3}{y^3} \cdot \left( {{x^4} - {y^4}} \right)\)

\( = {x^3}{y^4} \cdot {x^2} - {x^3}{y^4} \cdot 2{y^3} - 2{x^3}{y^3} \cdot {x^4} + 2{x^3}{y^3} \cdot {y^4}\)

\( = {x^5}{y^4} - 2{x^3}{y^7} - 2{x^7}{y^3} + 2{x^3}{y^7}\)

\( = {x^5}{y^4} - 2{x^7}{y^3}\)

c) \({\left( {2x - 3} \right)^2} - 2\left( {2x - 3} \right)\left( {2x - 1} \right) + {\left( {2x - 1} \right)^2}\)

\( = {\left[ {\left( {2x - 3} \right) - \left( {2x - 1} \right)} \right]^2}\)

\( = {\left( {2x - 3 - 2x + 1} \right)^2}\)

\( = {\left( { - 2} \right)^2}\) \( = 4\)