جد ناتج الضرب في كل مما يأتي:

$\sqrt{2}{x}^2{y}^2(\sqrt{2}x{y}^5-y^5)$

$\begin{array}{rl}& \left(\sqrt{2}{\mathrm{x}}^2{\mathrm{y}}^2\right)\left(\sqrt{2}{\mathrm{xy}}^5\right)-\left(\sqrt{2}{\mathrm{x}}^2{\mathrm{y}}^2\right)\left({\mathrm{y}}^5\right)\\ & =\left(\sqrt{2}\sqrt{2}\right)({\mathrm{x}}^2\cdot \mathrm{x}\left({\mathrm{y}}^2{\mathrm{y}}^5\right)-\sqrt{2}{\mathrm{x}}^2({\mathrm{y}}^2\cdot {\mathrm{y}}^5)\\ & =2{\mathrm{x}}^3{\mathrm{y}}^7-\sqrt{2}{\mathrm{x}}^2{\mathrm{y}}^7\end{array}$

تأكد من فهمك

جد ناتج الضرب في كل مما يأتي:

$\left(\frac{\sqrt{3}}{4}{m}^{2}n\right)\left(2m^3\right)$

$\frac{\sqrt{3}}{2}{m}^{5}n$

$\left(20x^{-5}yz\right)\left(10xy\right)$

$200x^{-4}{y}^{2}z$

$\left(8r^3{v}^2\right)\left(\right|-5|r^{2}v+6r^2{v}^2)$

$40r^{5}v3+48r^5{v}^4$

$\sqrt{2}{x}^2{y}^2(\sqrt{2}x{y}^5-y^5)$

$\begin{array}{rl}& \left(\sqrt{2}{\mathrm{x}}^2{\mathrm{y}}^2\right)\left(\sqrt{2}{\mathrm{xy}}^5\right)-\left(\sqrt{2}{\mathrm{x}}^2{\mathrm{y}}^2\right)\left({\mathrm{y}}^5\right)\\ & =\left(\sqrt{2}\sqrt{2}\right)({\mathrm{x}}^2\cdot \mathrm{x}\left({\mathrm{y}}^2{\mathrm{y}}^5\right)-\sqrt{2}{\mathrm{x}}^2({\mathrm{y}}^2\cdot {\mathrm{y}}^5)\\ & =2{\mathrm{x}}^3{\mathrm{y}}^7-\sqrt{2}{\mathrm{x}}^2{\mathrm{y}}^7\end{array}$

$\sqrt{7}{\mathrm{z}}^2\mathrm{w}({\mathrm{z}}^{-1}\mathrm{wy}+2\sqrt{7}{\mathrm{z}}^4{\mathrm{w}}^2\mathrm{y})$

$\begin{array}{rl}& \left(\sqrt{7}{2}^{2}w\right)\left(2^{-1}wy\right)+\left(\sqrt{72}{2}^{3}w\right)\left(2\sqrt{7}{2}^{4}wr\right)\\ & =\sqrt{7}{z}^{2-1}{w}^{1+1}y+2\sqrt{7}\cdot \sqrt{7}{z}^{2+4}\cdot w^{1+1}y\\ & =\sqrt{7}2w^{2}y+{142}^6{w}^{2}y\end{array}$

$\frac{1}{4}{h}^{2}k(\frac{\sqrt{16}}{4}{h}^{-2}kr+6h^3{k}^{-1}{r}^2+\sqrt{8})$

$$\begin{gathered} \left(\frac{1}{4}{H}^{2}K\right)\left(\frac{\sqrt{16}}{4}{H}^{-2}KR\right)+\left(\frac{1}{4}{H}^{2}K\right)\left(6H{K}^{-t}{R}^2\right)+\left(\frac{1}{4}{H}^{2}K\right)\left(\sqrt{8}\right) \\ \begin{array}{rl}& {=}_4^1{H}^{2-2}{K}^{1+1}R+\frac{6}{4}{H}^{2+3}{K}^{1-1}{R}^2{+}_4^{\sqrt{8}}{H}^{2}K\\ & =\frac{1}{4}{K}^{2}R{+}_3^2{H}^5{R}^2{+}_2^{\sqrt{2}}{H}^{2}K\end{array} \end{gathered}$$