تدرب وحل التمرينات

احسب قيمة كل مقدار جبري إذا علمت أن قيمة a=9 , b=15 , x=3 , y=8

$b^2-5xy$

$\begin{array}{rl}{B}^2-5XY& =(15{)}^2-5(3\left)\right(8)\\ & =225-120=105\end{array}$

$4\mathrm{b}-5\mathrm{a}$

$\begin{array}{rl}& 4B-5A\\ & =4\left(15\right)-5\left(9\right)=60-45=15\end{array}$

$2ab$

$2AB=2\left(9\right)\left(15\right)=270$

$4y+8x-6$

$\begin{array}{rl}& 4y+8x-6=4\left(8\right)+8\left(3\right)-6\\ & =32+24-6=50\end{array}$

$7y÷4+5x$

$\begin{array}{rl}& 7y÷4+5x\\ & =7\left(8\right)÷4+5\left(3\right)\\ & =56÷4+15=14+15=29\end{array}$

${\mathrm{y}}^2-5\mathrm{a}$

$\begin{array}{rl}& y^2-5A\\ & =(8{)}^2-5(9)=64-45=19\end{array}$

اختر الإجابة الصحيحة لقيمة المقدار الجبري لكل مما يأتي:

$x^3+y^3,......,x=2,y=4$

$\begin{array}{rl}& (2{)}^3+(4{)}^3\\ & =8+64=72\end{array}$

$x^4+y^3-z^3+w,......,\mathrm{w}=2,\mathrm{x}=1,\mathrm{y}=2,\mathrm{z}=-6$

$\begin{array}{rl}& (1{)}^4+(2{)}^3-(-6{)}^3+(2)\\ =& 1+8+216+2=227\end{array}$

$\frac{\mathrm{x}+\mathrm{y}}{{\mathrm{z}}^2},......,x=8,y=2,z=5$

$\frac{8+2}{(5{)}^2}=\frac{10}{25}=\frac{2}{5}$

$|x-y|,......x=-8,y=-3$

$\begin{array}{rl}& |-8-(-3\left)\right|=|-8+3|\\ & =|-5|=5\end{array}$

$\sqrt{x}+\sqrt[3]{7-y},......,x=1,y=8$

$$\begin{gathered} \sqrt{1}+\sqrt[3]{7-8}=1+\sqrt[3]{-1} \\ =1+(-1)=0 \end{gathered}$$