[3-3] ضرب المقادير الجبرية

اختر الإجابة الصحيحة لكل مما يأتي:

جد ناتج الضرب لكل مما يأتي:

$(x-5)(x+5)$

• $x^2+25$
• ${\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{25}$
• $x^2-10x+25$
• $x^2+5x-25$

$(\frac{1}{3}{m}^2-9)(\frac{1}{3}{m}^2+6)$

• $\begin{array}{rl}& \frac{1}{9}{m}^4-\frac{15}{3}{m}^2+63\end{array}$
• $\begin{array}{rl}& \frac{1}{9}{m}^4+m^2+63\end{array}$
• $\begin{array}{rl}& \frac{1}{9}{m}^4-\frac{15}{3}{m}^2-63\end{array}$
• $\begin{array}{rl}& \frac{\mathbf{1}}{\mathbf{9}}{\mathbf{m}}^{\mathbf{4}}\mathbf{-}{\mathbf{m}}^{\mathbf{2}}\mathbf{-}\mathbf{63}\end{array}$

$(\sqrt[3]{8}{n}^2+10)(\sqrt[3]{27}{n}^2-5)$

• $\begin{array}{rl}& 6n^4-20n^2-50\end{array}$
• $\begin{array}{rl}& 6n^4-40n^2+50\end{array}$
• $\begin{array}{rl}& \mathbf{6}{\mathbf{n}}^{\mathbf{4}}\mathbf{+}\mathbf{20}{\mathbf{n}}^{\mathbf{2}}\mathbf{-}\mathbf{50}\end{array}$
• $\begin{array}{rl}& 6n^4+20n^2+50\end{array}$

$\begin{array}{rl}& (z-\sqrt{5})(z+\sqrt{5})\end{array}$

• ${\mathbf{z}}^{\mathbf{2}}\mathbf{-}\mathbf{5}$
• ${\mathrm{z}}^2+5$
• ${\mathrm{z}}^2+\sqrt{25}\mathrm{z}+5$
• $z^2-\sqrt{25}\mathrm{z}-5$

$\begin{array}{rl}& \left(\right|-4|gh-3)\left(\right|4|gh+3)\end{array}$

• $\begin{array}{rl}& 16g^2{h}^2+gh+9\end{array}$
• $\begin{array}{rl}& 16{\mathrm{g}}^2{\mathrm{h}}^2-\mathrm{gh}+9\end{array}$
• $\begin{array}{rl}& 16g^2{h}^2+9\end{array}$
• $\begin{array}{rl}& \mathbf{16}{\mathbf{g}}^{\mathbf{2}}{\mathbf{h}}^{\mathbf{2}}\mathbf{-}\mathbf{9}\end{array}$

$(-2x^2+7)(x^2+x-4)$

• $\begin{array}{rl}& 2x^4+2x^3+x^2+7x+28\end{array}$
• $\begin{array}{rl}& \mathbf{-}\mathbf{2}{\mathbf{x}}^{\mathbf{4}}\mathbf{-}\mathbf{2}{\mathbf{x}}^{\mathbf{3}}\mathbf{+}\mathbf{15}{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{7}\mathbf{x}\mathbf{-}\mathbf{28}\end{array}$
• $\begin{array}{rl}& -2x^4-2x^3+x^2+7x+28\end{array}$
• $\begin{array}{rl}& 2x^4-2x^3-x^2-7x+28\end{array}$

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

• $\begin{array}{rl}& 8x^3+27\end{array}$
• $\begin{array}{rl}& \frac{1}{8}{x}^3+27\end{array}$
• $\begin{array}{rl}& 8x^3-27\end{array}$
• $\begin{array}{rl}& \frac{\mathbf{1}}{\mathbf{8}}{\mathbf{x}}^{\mathbf{3}}\mathbf{-}\mathbf{27}\end{array}$

$(w^2+\sqrt{3})(2w^2-w-\sqrt{3})$

• $\begin{array}{rl}& 2w^4+w^3+2\sqrt{3}{w}^2-\sqrt{3}w+3\end{array}$
• $\begin{array}{rl}& 2w^4-w^3+2\sqrt{3}{w}^2+\sqrt{3}w-3\end{array}$
• $\begin{array}{rl}& \mathbf{2}{\mathbf{w}}^{\mathbf{4}}\mathbf{-}{\mathbf{w}}^{\mathbf{3}}\mathbf{+}\sqrt{\mathbf{3}}{\mathbf{w}}^{\mathbf{2}}\mathbf{-}\sqrt{\mathbf{3}}\mathbf{w}\mathbf{-}\mathbf{3}\end{array}$
• $\begin{array}{rl}& 2w^4+w^3+2\sqrt{3}{w}^2+\sqrt{3}w-3\end{array}$

$(3\mathrm{k}+\sqrt[3]{5})(9{\mathrm{k}}^2-3\sqrt[3]{5}\mathrm{k}+\sqrt[3]{25})$

• $(27k^3+25)$
• $\mathbf{(}\mathbf{27}{\mathit{k}}^{\mathbf{3}}\mathbf{+}\mathbf{5}\mathbf{)}$
• $(27k^3-25)$
• $(27k^3-5)$

$(2y-1)(4y^2+2y+1)$

• $\mathbf{8}{\mathit{y}}^{\mathbf{3}}\mathbf{-}\mathbf{1}$
• $y^3-8$
• $8y^3+1$
• $y^3+8$