Lời giải

a) Các biểu thức là đơn thức là: \(\frac{{\sqrt 2 }}{{11}}x; - 3x{y^4}z\).

b) Các biểu thức là đa thức là: \(\frac{{ - 13}}{{21}}{x^3}{y^2} + 9x{y^6} - 8;x + y;xyz + \sqrt 2 \).

Lời giải

a) \(\frac{{ - 9}}{{17}}{x^{23}}{y^{22}}{y^{14}} = \frac{{ - 9}}{{17}}{x^{23}}\left( {{y^{22}}.{y^{14}}} \right) = \frac{{ - 9}}{{17}}{x^{23}}{y^{36}}\).

b) \(\frac{2}{{\sqrt {121} }}x{y^3}z{y^2}{z^3} = \frac{2}{{\sqrt {{{11}^2}} }}x\left( {{y^3}.{y^2}} \right)\left( {z.{z^3}} \right) = \frac{2}{{11}}x{y^5}{z^4}\).

c) \(\frac{{ - 187}}{{124}}{x^4}{y^6}{z^8}{x^5}{y^2}{z^{10}} = \frac{{ - 187}}{{124}}\left( {{x^4}.{x^5}} \right)\left( {{y^6}.{y^2}} \right)\left( {{z^8}.{z^{10}}} \right) = \frac{{ - 187}}{{124}}{x^9}{y^8}{z^{18}}\).

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

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

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

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

Lời giải

a) \({x^2}{y^5} + 2x{y^2} - {x^2}{y^5} + \frac{{24}}{{35}}x{y^2}\)

\( = \left( {{x^2}{y^5} - {x^2}{y^5}} \right) + \left( {2x{y^2} + \frac{{24}}{{35}}x{y^2}} \right)\)

\[ = 0 + \left( {2 + \frac{{24}}{{35}}} \right)x{y^2}\]

\( = \frac{{94}}{{35}}x{y^2}\).

b) ‒11y²z³ ‒ 22xy³z³ + 2y²z³ ‒ 33xy³z³ ‒ 72

= (‒11y²z³ + 2y²z³) + (‒ 22xy³z³ ‒ 33xy³z³) ‒ 72

= ‒9y²z³ ‒ 55xy³z³ ‒ 72.

c) \(\frac{{\sqrt 4 }}{{41}}{x^2}{y^4}{z^3} + {x^2}{y^4}z + \frac{{39}}{{41}}{x^2}{y^4}{z^3} - {x^2}{y^4}z + {z^{18}}\)

\( = \frac{2}{{41}}{x^2}{y^4}{z^3} + {x^2}{y^4}z + \frac{{39}}{{41}}{x^2}{y^4}{z^3} - {x^2}{y^4}z + {z^{18}}\)

\( = \left( {\frac{2}{{41}}{x^2}{y^4}{z^3} + \frac{{39}}{{41}}{x^2}{y^4}{z^3}} \right) + \left( {{x^2}{y^4}z - {x^2}{y^4}z} \right) + {z^{18}}\)

\( = {x^2}{y^4}{z^3} + {z^{18}}\).

Lời giải

a) Thay \(x = 2;y = \frac{1}{2}\) vào A, ta có:

\(A = - {2^3}.{\left( {\frac{1}{2}} \right)^2} + {2.2^2}.{\left( {\frac{1}{2}} \right)^5} - \frac{1}{2}.2.\frac{1}{2}\)

 \( = - {2^3}.\frac{1}{{{2^2}}} + {2^3}.\frac{1}{{{2^5}}} - \frac{1}{2} = - 2 + \frac{1}{4} - \frac{1}{2} = \frac{{ - 9}}{4}\).

b) Thay x = 99 và y = 0 vào B, ta có:

\(B = {0^{12}} + {99^5}{.0^5} - {100.99^4}{.0^4} + {100.99^3}{.0^3} - {100.99^2}{.0^2} + 100.99.0 - \sqrt {36} \)

 \( = - \sqrt {36} = - 6\).

c) Thay \(x = \frac{{ - 1}}{2};y = - \sqrt 3 ;z = 2\)vào C ta có:

\[C = \frac{{ - 1}}{2}.{\left( { - \sqrt 3 } \right)^2} + {5^2}.\frac{{ - 1}}{2}.2 - \sqrt 3 .\frac{{ - 1}}{2}.\left( { - \sqrt 3 } \right){.2^3} + 25\]

 \( = \frac{{ - 1}}{2}.3 + 25.\left( { - 1} \right) + 3.\left( { - 1} \right){.2^2} + 25 = \frac{{ - 3}}{2} - 25 - 12 + 25 = \frac{{ - 27}}{2}\).