Множење монома

Задаци

Текст задатака објашњених у видео лекцији:

Пр.1)   Израчунати следеће производе:

           а) $- 5{x^9} \cdot 11{x^3}$

           б) $- 8{n^5} \cdot \left( { - \frac{1}{2}{n^4}} \right)$

           в) $0,2x \cdot \left( { - 5{x^9}} \right)$

           г) $- 3{a^3}{b^6}{c^9} \cdot 12{a^4}{b^7}c$

           д) $\left( { - \frac{1}{4}{m^2}{n^4}{p^6}} \right) \cdot \left( {1\frac{1}{3}m{p^5}{n^4}} \right)$

Пр.2)   Упростити изразе:

           а) ${\left( { - 4{x^3}} \right)^2} \cdot 9{x^5}$

           б) ${\left( { - 6{x^5}} \right)^2} \cdot {\left( { - \frac{1}{2}{x^4}} \right)^3}$

           в) ${\left( {0,1{x^2}y} \right)^2} \cdot {\left( { - 5x{y^2}} \right)^3}$

Пр.3)   Квадрат монома $- 5a{b^2}$ увећати за производ монома $4ab$

           и $- 6a{b^3}$.

Пр.4)   Упростити израз

            $\left( { - \frac{3}{5}{m^2}n} \right) \cdot \left( {3\frac{1}{3}{m^3}{n^5}} \right) + \left( { - \frac{5}{6}m{n^2}} \right) \cdot \left( { - 1\frac{1}{5}{m^4}{n^4}} \right)$,

            а затим израчунати његову бројевну вредност за $m = 1$ и

            $n = - \sqrt 2$.

Пр.1)  

           а) $- 5{x^9} \cdot 11{x^3} = - 55{x^{12}}$

           б) $- 8{n^5} \cdot \left( { - \frac{1}{2}{n^4}} \right) = 4{n^9}$

           в) $0,2x \cdot \left( { - 5{x^9}} \right) = - 1{x^{10}} = - {x^{10}}$

           г) $- 3{a^3}{b^6}{c^9} \cdot 12{a^4}{b^7}c = - 36{a^7}{b^{13}}{c^{10}}$

           д) $\left( { - \frac{1}{4}{m^2}{n^4}{p^6}} \right) \cdot \left( {1\frac{1}{3}m{p^5}{n^4}} \right) = \left( { - \frac{1}{4}{m^2}{n^4}{p^6}} \right) \cdot \left( {\frac{4}{3}m{p^5}{n^4}} \right) = - \frac{1}{3}{m^3}{n^8}{p^{11}}$

Пр.2)   

           а) ${\left( { - 4{x^3}} \right)^2} \cdot 9{x^5} = {\left( { - 4} \right)^2}{\left( {{x^3}} \right)^2} \cdot 9{x^5} = 16 \cdot {x^6} \cdot 9{x^5} = 144{x^{11}}$

           б) ${\left( { - 6{x^5}} \right)^2} \cdot {\left( { - \frac{1}{2}{x^4}} \right)^3} = 36{x^{10}} \cdot \left( { - \frac{1}{8}} \right){x^{12}} = - \frac{9}{2}{x^{22}}$

           в) ${\left( {0,1{x^2}y} \right)^2} \cdot {\left( { - 5x{y^2}} \right)^3} = 0,01{x^4}{y^2} \cdot \left( { - 125{x^3}{y^6}} \right) = - 1,25{x^7}{y^8}$

Пр.3)   $${\left( { - 5a{b^2}} \right)^2} + 4ab\left( { - 6a{b^3}} \right) = 25{a^2}{b^4} - 24{a^2}{b^4} = {a^2}{b^4}$$

Пр.4)   Упростити израз

            $\left( { - \frac{3}{5}{m^2}n} \right) \cdot \left( {3\frac{1}{3}{m^3}{n^5}} \right) + \left( { - \frac{5}{6}m{n^2}} \right) \cdot \left( { - 1\frac{1}{5}{m^4}{n^4}} \right)$,

            а затим израчунати његову бројевну вредност за $m = 1$ и

            $n = - \sqrt 2$.

$$\begin{aligned}&\left( { - \frac{3}{5}{m^2}n} \right) \cdot \left( {3\frac{1}{3}{m^3}{n^5}} \right) + \left( { - \frac{5}{6}m{n^2}} \right) \cdot \left( { - 1\frac{1}{5}{m^4}{n^4}} \right) = \\ &= \left( { - \frac{3}{5}{m^2}n} \right) \cdot \left( {\frac{{10}}{3}{m^3}{n^5}} \right) + \left( { - \frac{5}{6}m{n^2}} \right) \cdot \left( { - \frac{6}{5}{m^4}{n^4}} \right) = \\ &= - 2{m^5}{n^6} + {m^5}{n^6} = - {m^5}{n^6} \\ & \\ &- {m^5}{n^6} = - {1^5}{\left( { - \sqrt 2 } \right)^6} = - \left[ {\left( { - \sqrt 2 } \right)\left( { - \sqrt 2 } \right)} \right] \cdot \left[ {\left( { - \sqrt 2 } \right)\left( { - \sqrt 2 } \right)} \right] \cdot \left[ {\left( { - \sqrt 2 } \right)\left( { - \sqrt 2 } \right)} \right] = \\ &= - 2 \cdot 2 \cdot 2 = - 8\end{aligned}$$