جد ناتج جمع الحدود الجبرية الآتية:

$x^2{y}^{2}z+\frac{1}{3}{x}^2{y}^{2}z+6x^2{y}^{2}z$

$\begin{array}{rl}& (1+\frac{1}{3}+6)x^2{y}^{2}z\\ & =\frac{3+1+18}{3}{x}^2{y}^{2}z\\ & =\frac{22}{3}{x}^2{y}^{2}z\end{array}$

الاختبار القبلي

اكتب المعامل (م) والمتغير (غ) في الحدود الجبرية الآتية:

المتغير ........ المعامل ........ $|-2|\mathrm{xy}$

المتغير XY المعامل |2-|

المتغير ........ المعامل ........ $30r^2{v}^2$

المتغير $R^2{y}^2$ المعامل 30

المتغير ........ المعامل ........ $\sqrt{16}{\mathrm{h}}^3{\mathrm{k}}^2$

المتغير $H^3{K}^3$ المعامل $\sqrt{16}$

المتغير ........ المعامل ........ $\frac{1}{2}{z}^{2}y$

المتغير $z^{2}y$ المعامل $\frac{1}{2}$

المتغير ........ المعامل ........ $10w^{3}h$

المتغير $w^{3}H$ المعامل 10

المتغير ........ المعامل ........ ${\mathrm{w}}^5{\mathrm{Z}}^2$

المتغير $w^5{z}^2$ المعامل 1

جد ناتج جمع الحدود الجبرية الآتية:

$5{\mathrm{h}}^2\mathrm{k}+10{\mathrm{h}}^2\mathrm{k}+\frac{1}{2}{\mathrm{h}}^2\mathrm{k}+|-\frac{1}{5}|{\mathrm{h}}^2\mathrm{k}$

$\begin{array}{rl}& (5+10+\frac{1}{2}+|-\frac{1}{5}|H^{2}K\\ & =(15+\frac{1}{2}+\frac{1}{5})H^{2}K\\ & =\frac{150+5+2}{10}{H}^{2}K\\ & =\frac{157}{10}{H}^{2}K\end{array}$

$x^2{y}^{2}z+\frac{1}{3}{x}^2{y}^{2}z+6x^2{y}^{2}z$

$\begin{array}{rl}& (1+\frac{1}{3}+6)x^2{y}^{2}z\\ & =\frac{3+1+18}{3}{x}^2{y}^{2}z\\ & =\frac{22}{3}{x}^2{y}^{2}z\end{array}$

$2r^{2}v+\frac{1}{4}{r}^{2}v+16r^{2}v+|-\frac{1}{2}|r^{2}v$

$\begin{array}{rl}& 2R^{2}V+\frac{1}{4}{R}^{2}V+16R^{2}V+|-\frac{1}{2}|R^{2}V=(2+\frac{1}{4}+16+|-\frac{1}{2}|)R^{2}V\\ & =(18+\frac{1}{4}+\frac{1}{2})R^{2}V=\frac{72+1+2}{4}{R}^{2}V=\frac{75}{4}{R}^{2}V\end{array}$

$|-7|a^{2}b+14a^{2}b+\frac{1}{28}{a}^{2}b$

$\begin{array}{rl}& |-7|A^{2}B+14A^{2}B+\frac{1}{28}{A}^{2}B=\left(\right|-7|+14+\frac{1}{28})A^{2}B\\ & =(7+14+\frac{1}{28})A^{2}B=(21+\frac{1}{28})A^{2}B=\frac{589}{28}{A}^{2}B\end{array}$

$10xy+\frac{1}{20}xy+\frac{1}{5}xy+4xy$

$\begin{array}{rl}& 10xy+\frac{1}{20}Xy+\frac{1}{5}xy+4xy=(10+\frac{1}{20}+\frac{1}{5}+4)xy\\ & \frac{200+1+4+80}{20}xy=\frac{285}{20}xy=\frac{57}{4}xy\end{array}$

$7a^2{b}^{2}z+|-18|a^2{b}^{2}z+9a^2{b}^{2}z$

$\begin{array}{rl}& 7A^2{B}^{2}Z+|-18|A^2{B}^{2}Z+9A^2{B}^{2}Z=(7+|-18|+9)A^2{B}^{2}Z\\ & =(7+18+9)A^2{B}^{2}Z=34A^2{B}^{2}Z\end{array}$

$2x^4{y}^2+\frac{1}{5}{x}^4{y}^2+|-\frac{1}{5}|x^4{y}^2$

$\begin{array}{rl}& 2x^4{y}^2+\frac{1}{5}{x}^4{y}^2+|-\frac{1}{5}|x^4{y}^2=(2+\frac{1}{5}+|-\frac{1}{5}|x^4{y}^2\\ & =(2+\frac{1}{5}+\frac{1}{5})x^4{y}^2=\frac{10+1+1}{5}{x}^4{y}^2=\frac{12}{5}{x}^4{y}^2\end{array}$

$12{\mathrm{g}}^2{\mathrm{h}}^2+\frac{1}{3}{\mathrm{g}}^2{\mathrm{h}}^2+\frac{1}{4}{\mathrm{g}}^2{\mathrm{h}}^2$

$\begin{array}{rl}& 12G^2{H}^2+\frac{1}{3}{G}^2{H}^2+\frac{1}{4}{G}^2{H}^2=(12+\frac{1}{3}+\frac{1}{4})G^2{H}^2\\ & =\frac{144+4+3}{12}{G}^2{H}^2=\frac{151}{12}{G}^2{H}^2\end{array}$

جد ناتج طرح الحدود الجبرية الآتية:

$\frac{1}{25}{h}^{2}k-15h^{2}k-5h^{2}k-|-\frac{1}{5}|h^{2}k$

$\begin{array}{rl}& \frac{1}{25}{H}^{2}K-15H^{2}K-5H^{2}K-|-\frac{1}{5}|H^{2}K=(\frac{1}{25}-15-5-|-\frac{1}{5}|H^{2}K\\ & =(\frac{1}{25}-20-\frac{1}{5})H^{2}K=\frac{1-500-5}{25}{H}^{2}K=\frac{-504}{25}{H}^{2}K\end{array}$

$16r^2{v}^2-\frac{1}{32}{r}^2{v}^2-64r^2{v}^2$

$\begin{array}{rl}& 16R^2{V}^2-\frac{1}{32}{R}^2{y}^2-64R^2{y}^2=(16-\frac{1}{32}-64)R^2{V}^2\\ & =(-48-\frac{1}{32})R^2{V}^2=\frac{-1536-1}{32}{R}^2{V}^2=\frac{-1537}{32}{R}^2{y}^2\end{array}$

$\frac{2}{3}xy-\frac{10}{6}xy-|-\frac{1}{3}|xy$

$\begin{array}{rl}& \frac{2}{3}xy-\frac{10}{6}xy-|-\frac{1}{3}|xy=(\frac{2}{3}-\frac{10}{6}-\mid -\frac{1}{3})xy\\ & =(\frac{2}{3}-\frac{5}{3}-\frac{1}{3})xy=\frac{2-5-1}{3}xy=\frac{-4}{3}xy\end{array}$

$30a^2{b}^2-5a^2{b}^2-15a^2{b}^2$

$30A^2{B}^2-5A^2{B}^2-15A^2{B}^2=(30-5-15)A^2{B}^2=10A^2{B}^2$

$|-15|z^2{v}^2-|-35|z^2{v}^2-5z^2{v}^2$

$\begin{array}{rl}& |-15|z^2{y}^2-|-35|z^2{v}^2-5z^2{y}^2=\left(\right|-15|-|-35|-5)z^2{v}^2\\ & =(15-35-5)z^2{v}^2=-25z^2{y}^2\end{array}$

$24w^{2}z-\sqrt{144}{w}^{2}z-9w^{2}z$

$\begin{array}{rl}& 24w^{2}z-\sqrt{144}{w}^{2}z-9w^{2}z=(24-\sqrt{144}-9)w^{2}z\\ & =(24-12-9)w^{2}z=3w^{2}z\end{array}$

جد ناتج ضرب الحدود الجبرية الآتية:

$\left(2x\right)\left(20y\right)$

$\left(2x\right)\left(20y\right)=\left(2x20\right)\left(xy\right)=40xy$

$\left(6z^2\right)\left(3v^2\right)$

$\left(6z^2\right)\left(3y^2\right)=\left(\right(6)\cdot (3\left)\right)\left(2^2{y}^2\right)=18z^2{y}^2$

$\left(\right|-20\left|\mathrm{z}\right)\left({\mathrm{r}}^3{\mathrm{v}}^3\right)$

$(-20\mid z)\left(R^3{v}^3\right)=\left(202\right)\left(R^3{v}^3\right)=202R^3{v}^3$

$10y(2x+60z+4)$

$\begin{array}{rl}& 10y(2x+60z+4)=\left(10y\right)\left(2x\right)+\left(10y\right)\left(60z\right)+\left(10y\right)\left(4\right)\\ & =20yx+600yx+40y\end{array}$

$|-2|\mathrm{xy}30{\mathrm{z}}^2(\frac{1}{3}{\mathrm{v}}^2+\frac{1}{15}{\mathrm{v}}^3\mathrm{y}+\frac{2}{30}\mathrm{mn})$

$\begin{array}{rl}& \left(30z^2\right)\left(\frac{1}{3}{v}^2\right)+\left(30z^2\right)\left(\frac{1}{15}{v}^{3}y\right)+\left(30z^2\right)\left(\frac{2}{30}MN\right)\\ & =10z^2{v}^2+2z^2{v}^{2}y+2z^{2}MN\end{array}$

$3y(20m^{2}n+4)$

$3y(20M^{2}N+4)=\left(3y\right)\left(20M^{2}N\right)+\left(3y\right)\left(4\right)=60Y{M}^{2}N+12y$

جد القيمة العددية للمقادير الجبرية الآتية:

$|-2|\mathrm{xy}\frac{1}{2}{\mathrm{z}}^2{\mathrm{y}}^2+3\mathrm{zy}+\mathrm{w};\mathrm{w}=2,\mathrm{z}=4,\mathrm{y}=3$

$\frac{1}{2}\left(4{)}^2\right(3{)}^2+3\left(4\right)\left(3\right)+2=\frac{1}{2}\times 16\times 9+24+2=72+24+2=98$

$3{\mathrm{h}}^3{\mathrm{k}}^2-5\mathrm{h}+4;\mathrm{h}=5,\mathrm{k}=3$

$3\left(5{)}^3\right(3{)}^2-5\left(5\right)+4=3\times 125\times 9-25+4=3354$

$|-25|r^2{v}^2+\frac{1}{3}v+5;r=1,v=12$

$|-25|\left(1{)}^2\right(12{)}^2+\frac{1}{3}\left(1\right)+5=25\times 144+\frac{1}{3}+5=3605.33$

$3xy-2xy+6;x=2,y=10$

$3\left(2\right)\left(10\right)-2\left(2\right)\left(10\right)+6=60-40+6=26$

جد المخرجات لقاعدة الدالة للمدخلات الآتية: