Thực hiện các phép tính:

a) \(2{x^2}{y^3} \cdot \left( {5xy - 4x} \right) - 10{x^3}{y^4}.\) b) \(4 \cdot \left( {10x - 3} \right) + {\left( {x + 5} \right)^2}.\)

c) \(\frac{{{x^2} + 3}}{{x - 2}} - \frac{{4x}}{{x - 2}} + \frac{1}{{x - 2}}.\)                                                       d) \(\frac{2}{{x - 3}} + \frac{3}{{x + 3}} + \frac{4}{{{x^2} - 9}}.\)

a) \(2{x^2}{y^3} \cdot \left( {5xy - 4x} \right) - 10{x^3}{y^4} = 10{x^3}{y^4} - 8{x^3}{y^3} - 10{x^3}{y^4} = - 8{x^3}{y^3}.\)

b) \(4 \cdot \left( {10x - 3} \right) + {\left( {x + 5} \right)^2} = 40x - 12 + {x^2} + 10x + 25 = {x^2} + 50x + 13.\)

c) \(\frac{{{x^2} + 3}}{{x - 2}} - \frac{{4x}}{{x - 2}} + \frac{1}{{x - 2}} = \frac{{{x^2} + 3 - 4x + 1}}{{x - 2}} = \frac{{{x^2} - 4x + 4}}{{x - 2}} = \frac{{{{\left( {x - 2} \right)}^2}}}{{x - 2}} = x - 2.\)                   

d) \(\frac{2}{{x - 3}} + \frac{3}{{x + 3}} + \frac{4}{{{x^2} - 9}} = \frac{{2\left( {x + 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} + \frac{{3\left( {x - 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} + \frac{4}{{\left( {x - 3} \right)\left( {x + 3} \right)}}\)

\[ = \frac{{2x + 6 + 3x - 9 + 4}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} = \frac{{5x + 1}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}.\]