[3-5] تحليل المقادير الجبرية

اختر الإجابة الصحيحة لكل مما يأتي:

حلل المقدار الجبري الآتي:

$81xy+72x$

• $\mathbf{9}\mathit{x}\mathbf{(}\mathbf{9}\mathit{y}\mathbf{+}\mathbf{8}\mathbf{)}$
• $9(9xy-8)$
• $9x(9xy-9)$
• $9x(9xy+9)$

$7z^3-z^2$

• $\begin{array}{rl}& 7{\mathrm{z}}^2(\mathrm{z}+\frac{1}{7})\end{array}$
• $7z^2(z+1)$
• $\begin{array}{rl}& \mathbf{7}{\mathbf{z}}^{\mathbf{2}}\mathbf{(}\mathbf{z}\mathbf{-}\frac{\mathbf{1}}{\mathbf{7}}\mathbf{)}\end{array}$
• $7z^2(z-1)$

$49g^2{h}^2+21gh$

• $\begin{array}{rl}& \mathbf{7}\mathbf{g}\mathbf{h}\mathbf{(}\mathbf{7}\mathbf{g}\mathbf{h}\mathbf{+}\mathbf{3}\mathbf{)}\end{array}$
• $\begin{array}{rl}& 7\mathrm{gh}(7\mathrm{gh}-3)\end{array}$
• $\begin{array}{rl}& 7(7\mathrm{gh}+3)\end{array}$
• $\begin{array}{rl}& 7(7{\mathrm{g}}^2{\mathrm{h}}^2+3\mathrm{gh}+1)\end{array}$

$11m^3{n}^2-44m^2{n}^2-121mn$

• $\begin{array}{rl}& mn(11m^2{n}^2-4mn-1)\end{array}$
• $11mn\left(m^2{n}^2-4mn-11\right)$
• $\begin{array}{rl}& \mathbf{11}\mathbf{m}\mathbf{n}\mathbf{(}{\mathbf{m}}^{\mathbf{2}}\mathbf{n}\mathbf{-}\mathbf{4}\mathbf{m}\mathbf{n}\mathbf{-}\mathbf{11}\mathbf{)}\end{array}$
• $11\left(11m^2{n}^2-4mn-1\right)$

$150r^3{v}^2+25rv+75r^2{v}^2$

• $\mathbf{25}\mathit{r}\mathit{v}\left(6r^{2}v+1+3rv\right)$
• $25\text{rv}(6rv+3rv-1)$
• $75\mathrm{rv}(2\mathrm{rv}+1)$
• $75\mathrm{rv}(2{\mathrm{r}}^2\mathrm{v}+13+\mathrm{rv})$

$m^2-n^2$

• $\begin{array}{rl}& \mathbf{(}\mathbf{m}\mathbf{-}\mathbf{n}\mathbf{)}\mathbf{(}\mathbf{m}\mathbf{+}\mathbf{n}\mathbf{)}\end{array}$
• $\begin{array}{rl}& (\mathrm{m}+\mathrm{n})(\mathrm{m}+\mathrm{n})\end{array}$
• $\begin{array}{rl}& (m-n)(m-n)\end{array}$
• $\begin{array}{rl}& (\mathrm{m}+\mathrm{n}{)}^2\end{array}$

$4z^2-9w^2$

• $\begin{array}{rl}& (2z-3w)(2z-3w)\end{array}$
• $\begin{array}{rl}& \mathbf{(}\mathbf{2}\mathbf{z}\mathbf{-}\mathbf{3}\mathbf{w}\mathbf{)}\mathbf{(}\mathbf{2}\mathbf{z}\mathbf{+}\mathbf{3}\mathbf{w}\mathbf{)}\end{array}$
• $\begin{array}{rl}& (2z+3w)(2z+3w)\end{array}$
• $\begin{array}{rl}& (2z+3w{)}^2\end{array}$

$36r^2-25v^2$

• $\begin{array}{rl}& (6\mathrm{r}+5\mathrm{v})(6\mathrm{r}+5)\end{array}$
• $\begin{array}{rl}& \mathbf{(}\mathbf{6}\mathbf{r}\mathbf{-}\mathbf{5}\mathbf{v}\mathbf{)}\mathbf{(}\mathbf{6}\mathbf{r}\mathbf{+}\mathbf{5}\mathbf{v}\mathbf{)}\end{array}$
• $\begin{array}{rl}& (6\mathrm{r}-5\mathrm{v})(6\mathrm{r}-5)\end{array}$
• $\begin{array}{rl}& (6r+5{)}^2\end{array}$

$81g^2{h}^2-64$

• $\begin{array}{rl}& \mathbf{(}\mathbf{9}\mathbf{g}\mathbf{h}\mathbf{+}\mathbf{8}\mathbf{)}\mathbf{(}\mathbf{9}\mathbf{g}\mathbf{h}\mathbf{-}\mathbf{8}\mathbf{)}\end{array}$
• $\begin{array}{rl}& (9\mathrm{gh}-8)(9\mathrm{gh}-8)\end{array}$
• $\begin{array}{rl}& (9\mathrm{gh}+8)(9\mathrm{gh}+8)\end{array}$
• $\begin{array}{rl}& (9\mathrm{gh}+8{)}^2\end{array}$

$50x^2-2$

• $\begin{array}{rl}& (5x+1)(5x+1)\end{array}$
• $\begin{array}{rl}& 2(25x^2+1)\end{array}$
• $\begin{array}{rl}& \mathbf{2}\mathbf{(}\mathbf{5}\mathbf{x}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{(}\mathbf{5}\mathbf{x}\mathbf{+}\mathbf{1}\mathbf{)}\end{array}$
• $\begin{array}{rl}& (5x-1)(5x-1)\end{array}$