اختر الإجابة الصحيحة لكل مما يأتي: حل المقادير الجبرية التالية باستعمال الجمع:

$(\sqrt{5}{y}^2{x}^2+6)+(3\sqrt{5}{x}^2{y}^2+9y+4)$

• $4\sqrt{5}{y}^2{x}^2+10$
• $\mathbf{2}\sqrt{\mathbf{5}}{\mathit{y}}^{\mathbf{3}}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{9}\mathit{y}\mathbf{+}\mathbf{10}$
• $4\sqrt{5}{y}^3{x}^2+10y$
• $4\sqrt{5}{y}^2{x}^2+9y+10$

[3-1] جمع المقادير الجبرية وطرحها

اختر الإجابة الصحيحة لكل مما يأتي:

حل المقادير الجبرية التالية باستعمال الجمع:

$(3x^2+4x+5)+(5x^2+x+6)$

• $\begin{array}{rl}& 2x^2+6x+30\end{array}$
• $\begin{array}{rl}& 8x^2+3x+1\end{array}$
• $\begin{array}{rl}& \mathbf{8}{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{5}\mathbf{x}\mathbf{+}\mathbf{11}\end{array}$
• $\begin{array}{rl}& 2x^2+5x+1\end{array}$

$(\sqrt{5}{y}^2{x}^2+6)+(3\sqrt{5}{x}^2{y}^2+9y+4)$

• $4\sqrt{5}{y}^2{x}^2+10$
• $\mathbf{2}\sqrt{\mathbf{5}}{\mathit{y}}^{\mathbf{3}}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{9}\mathit{y}\mathbf{+}\mathbf{10}$
• $4\sqrt{5}{y}^3{x}^2+10y$
• $4\sqrt{5}{y}^2{x}^2+9y+10$

$\left(\right|-2|z^{2}w+4k+\sqrt{7})+\left(\right|10|z^{2}w-10k+2\sqrt{7})$

• $8{\mathrm{z}}^2\mathrm{w}+6\mathrm{k}+3\sqrt{7}$
• $-12z^{2}w-6k+3\sqrt{7}$
• $\mathbf{12}{\mathbf{z}}^{\mathbf{2}}\mathbf{w}\mathbf{-}\mathbf{6}\mathbf{k}\mathbf{+}\mathbf{3}\sqrt{\mathbf{7}}$
• $-12z^{2}w-14k+3\sqrt{7}$

$(\frac{3}{4}{\mathrm{h}}^3\mathrm{k}+5\mathrm{gh}-3)+(\frac{2}{5}{\mathrm{h}}^3\mathrm{k}-10\mathrm{gh}+4)$

• $8{\mathrm{z}}^2\mathrm{w}+6\mathrm{k}+3\sqrt{7}$
• $\frac{23}{20}{h}^{3}k-15gh-1$
• $\frac{1}{5}{h}^{3}k-5gh+1$
• $\frac{\mathbf{23}}{\mathbf{20}}{\mathbf{h}}^{\mathbf{3}}\mathbf{k}\mathbf{-}\mathbf{5}\mathit{g}\mathit{h}\mathbf{+}\mathbf{1}$

حل المقادير الجبرية التالية باستعمال الطرح:

$(4m^2{n}^2-5)-(3m^2{n}^2+x+3)$

• $\begin{array}{rl}& m^2{n}^2+x+2\end{array}$
• $\begin{array}{rl}& 7m^2{n}^2-x-8\end{array}$
• $\begin{array}{rl}& m^2{n}^2-x+1\end{array}$
• $\begin{array}{rl}& {\mathbf{m}}^{\mathbf{2}}{\mathbf{n}}^{\mathbf{2}}\mathbf{-}\mathbf{x}\mathbf{-}\mathbf{8}\end{array}$

$(\sqrt{13}{g}^3{h}^4+z^2+20)-(5\sqrt{13}{g}^3{h}^4-4z^2+12)$

• $\begin{array}{rl}& 4\sqrt{13}{g}^3{h}^4+5{\mathrm{z}}^2+22\end{array}$
• $4\sqrt{13}{g}^3{h}^4+3z^2+8$
• $-4\sqrt{13}{g}^3{h}^4-5z^2+20$
• $\begin{array}{rl}& \mathbf{-}\mathbf{4}\sqrt{\mathbf{13}}{\mathbf{g}}^{\mathbf{3}}{\mathbf{h}}^{\mathbf{4}}\mathbf{+}\mathbf{5}{\mathbf{z}}^{\mathbf{2}}\mathbf{+}\mathbf{8}\end{array}$

$\left(\right|-24|yz+2x^2+12)-(6yz-15x^2-4)$

• $30yz+13x^2+16$
• $-18yz-13x^2+8$
• $\mathbf{18}\mathit{y}\mathit{z}\mathbf{+}\mathbf{17}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{16}$
• $18yz-13x^2+16$

$(\frac{6}{3}{x}^4+7mn-8)-(\frac{2}{3}{x}^4-10mn-2)$

• $\begin{array}{rl}& -\frac{4}{3}{x}^4-3mn+6\end{array}$
• $\frac{4}{3}{x}^4+3mn-6$
• $\frac{4}{3}{x}^4-17mn-6$
• $\begin{array}{rl}& \frac{\mathbf{4}}{\mathbf{3}}{\mathbf{x}}^{\mathbf{4}}\mathbf{+}\mathbf{17}\mathbf{m}\mathbf{n}\mathbf{-}\mathbf{6}\end{array}$