حلل كل مقدار من المقادير الجبرية الآتية إلى أبسط صورة:

$\frac{1}{27}{x}^3+\frac{1}{8}$

$\frac{1}{27}{x}^3+\frac{1}{8}=(\frac{1}{3}x+\frac{1}{2})(\frac{1}{9}{x}^2-\frac{1}{6}x+\frac{1}{4})$

تأكد من فهمك

(1)- حلل كل مقدار من المقادير الجبرية الآتية إلى أبسط صورة:

$y^3+216$

$y^3+216=y^3+6^3=(y+6)(y^2-6y+36)$

${\mathrm{x}}^3+{\mathrm{z}}^3$

$x^3+z^3=(x+z)(x^2-xz+z^2)$

$125+8z^3$

$125+8z^3=(5+2z)(25\cdot 10z+4z^2)$

$\frac{1}{27}{x}^3+\frac{1}{8}$

$\frac{1}{27}{x}^3+\frac{1}{8}=(\frac{1}{3}x+\frac{1}{2})(\frac{1}{9}{x}^2-\frac{1}{6}x+\frac{1}{4})$

$\frac{1}{a^3}+\frac{1}{64}$

$\frac{1}{a^3}+\frac{1}{64}=(\frac{1}{a}+\frac{1}{4})(\frac{1}{a^2}-\frac{1}{4a}+\frac{1}{16})$

$\frac{1}{3}{t}^3+9$

$\frac{1}{3}{t}^3+9=\frac{1}{3}(t^3+27)=\frac{1}{3}(t+3)(t^2-3t+9)$

$0.125+{\mathrm{v}}^3$

$0.125+v^3=(0.5+v)(0.25-0.5v+v^2)$

$1+0.008z^3$

$1+0.008{\mathrm{z}}^3=(1+0.2\mathrm{z})(1-0.2\mathrm{z}+0.04{\mathrm{z}}^2)$

(2)- حلل كل مقدار من المقادير الجبرية الآتية إلى أبسط صورة:

$a^3-8^3$

$a^3-8^3=(a-8)(a^2+8a+64)$

$8y^3-64$

$8y^3-64=8(y-2)(y^2+2y+4)$

$\frac{1}{c^3}-\frac{1}{8}$

$\frac{1}{c^3}-\frac{1}{8}=(\frac{1}{c}-\frac{1}{2})(\frac{1}{c^2}+\frac{1}{2c}+\frac{1}{4})$

$\frac{1}{2}{v}^3-4$

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

$0.125-{\mathrm{m}}^3$

$0.125-m^3=(0.5-m)(0.25+0.5m+m^2)$

$25-\frac{1}{5}{n}^3$

$\begin{array}{rl}25-\frac{1}{5}{\mathrm{n}}^3& =\frac{1}{5}(125-{\mathrm{n}}^3)\\ & =\frac{1}{5}(5-\mathrm{n})(25+5\mathrm{n}+{\mathrm{n}}^2)\end{array}$

$3b^3-81$

$3b^3-81=3(b^3-27)=3(b-3)(b^2+3b+9)$

$0.216{\mathrm{v}}^3-0.008{\mathrm{t}}^3$

$\begin{array}{rl}& 0.216{\mathrm{v}}^3-0.008{\mathrm{t}}^3\\ & =(0.6\mathrm{v}-0.2\mathrm{t})(0.36{\mathrm{v}}^2+0.12\mathrm{vt}+0.04{\mathrm{t}}^2)\end{array}$