Рационални алгебарски изрази 1

Текст задатака објашњених у видео лекцији.

Пр.1   $\left( {2 + 3x - {x^2}} \right)\left( {{x^2} + 5x - 1} \right) - 5{x^2}\left( {{x^2} - 2x + 3} \right) = $

Пр.2   $5x - 5a = $

           ${a^3} - {a^2} = $

           $6{x^2}{y^2} + 4{x^3}y = $

           ${a^3}{b^2} - 4a{b^5} + 2{a^4}{b^2} = $

           $14{a^7}{x^3} - 21{a^3}{x^8} + 84{a^4}{x^3} - 49{x^5}{a^6} = $

Пр.1 $\left( {2 + 3x - {x^2}} \right)\left( {{x^2} + 5x - 1} \right) - 5{x^2}\left( {{x^2} - 2x + 3} \right) = $

\[\begin{gathered}
= \left( {2 + 3x - {x^2}} \right)\left( {{x^2} + 5x - 1} \right) - 5{x^2}\left( {{x^2} - 2x - 3} \right) = \hfill \\
= 2{x^2} + 10x - 2 + 3{x^3} + 15{x^2} - 3x - {x^4} - 5{x^3} + \hfill \\
+ {x^2} - 5{x^4} + 10{x^3} - 15{x^2} = - 6{x^4} + 8{x^3} + 3{x^2} + 7x - 2 \hfill \\
\end{gathered} \]

Пр.2

$5x - 5a = 5\left( {x - a} \right)$

${a^3} - {a^2} = {a^2}\left( {a - 1} \right)$

$6{x^2}{y^2} + 4{x^3}y = 2{x^2}y\left( {3y + 2x} \right)$

${a^3}{b^2} - 4a{b^5} + 2{a^4}{b^2} = a{b^2}\left( {{a^2} - 4{b^3} + 2{a^3}} \right)$

$14{a^7}{x^3} - 21{a^3}{x^8} + 84{a^4}{x^3} - 49{x^5}{a^6} = $

\[ = 7{a^3}{x^3}\left( {2{a^4} - 3{x^5} + 12a - 7{a^3}{x^2}} \right)\]