Thực hiện phép tính:

a) xy³ ‒ 2xy³ ‒ 12xy³;

b) \(\frac{{ - 12}}{{43}}{x^2}y + 2{x^2}y + \frac{{ - 31}}{{43}}{x^2}y\);

c) \(\frac{{ - \sqrt {16} }}{{75}}{x^6}{y^9}z + \frac{{ - \sqrt {49} }}{{15}}{x^6}{y^9}z - \frac{1}{5}{x^6}{y^9}z\).

Lời giải

a) xy³ ‒ 2xy³ ‒ 12xy³ = (1 ‒ 2 ‒ 12)xy³ = ‒13xy³.

b) \(\frac{{ - 12}}{{43}}{x^2}y + 2{x^2}y + \frac{{ - 31}}{{43}}{x^2}y\)

\( = \left( {\frac{{ - 12}}{{43}} + \frac{{ - 31}}{{43}} + 2} \right){x^2}y\)

= (‒1 + 2)x²y

= x²y.

c) \(\frac{{ - \sqrt {16} }}{{75}}{x^6}{y^9}z + \frac{{ - \sqrt {49} }}{{15}}{x^6}{y^9}z - \frac{1}{5}{x^6}{y^9}z\)

\( = \frac{{ - 4}}{{75}}{x^6}{y^9}z - \frac{7}{{15}}{x^6}{y^9}z - \frac{1}{5}{x^6}{y^9}z\)

\( = \left( {\frac{{ - 4}}{{75}} - \frac{7}{{15}} - \frac{1}{5}} \right){x^6}{y^9}z\)

\( = \left( {\frac{{ - 4}}{{75}} - \frac{{35}}{{75}} - \frac{{15}}{{75}}} \right){x^6}{y^9}z = \frac{{ - 54}}{{75}}{x^6}{y^9}z = \frac{{ - 18}}{{25}}{x^6}{y^9}z\).