Thực hiện phép tính: a) ( 2x − 5 )^2 – 4x ( x − 5 ) ; b) ( 9x^4y^3 – 15x^3y^4 ) : 3x^2y^2 + 5xy^2 ;

Hướng dẫn giải:

a) 2x−52–4xx−5

\[ = \left( {4{x^2} - 20x + 25} \right) - \left( {4{x^2} - 20x} \right)\]

\[ = 4{x^2} - 20x + 25 - 4{x^2} + 20x = 25\].

b) 9x4y3–15x3y4:3x2y2+5xy2

\[ = 9{x^4}{y^3}:3{x^2}{y^2}--15{x^3}{y^4}:3{x^2}{y^2} + 5x{y^2}\]

=3x2y–5xy2+5xy2=3x2y

c) \(\frac{x}{{2x - 2}} - \frac{3}{{2x + 2}} + \frac{1}{{1 - {x^2}}}\) (MTC: \[2\left( {x - 1} \right)\left( {x + 1} \right)\])

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

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

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