Whakaoti i te [(sqrt{3})^2-2*(1/2)^2-3/4x(sqrt{2})^2-4(2/sqrt{3})^2]

$$[ ( \sqrt { 3 } ) ^ { 2 } - 2 \times ( \frac { 1 } { 2 } ) ^ { 2 } - \frac { 3 } { 4 } x ( \sqrt { 2 } ) ^ { 2 } - 4 ( \frac { 2 } { \sqrt { 3 } } ) ^ { 2 } ]$$

Aromātai

$$-\frac{3x}{2}-\frac{17}{6}$$

Ngā Upane Otinga

Ko te pūrua o \sqrt{3} ko 3.

$$3-2\times \left(\frac{1}{2}\right)^{2}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2}$$

Tātaihia te \frac{1}{2} mā te pū o 2, kia riro ko \frac{1}{4}.

$$3-2\times \frac{1}{4}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2}$$

Whakareatia te 2 ki te \frac{1}{4}, ka \frac{1}{2}.

$$3-\frac{1}{2}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2}$$

Tangohia te \frac{1}{2} i te 3, ka \frac{5}{2}.

$$\frac{5}{2}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{5}{2}-\frac{3}{4}x\times 2-4\times \left(\frac{2}{\sqrt{3}}\right)^{2}$$

Whakareatia te \frac{3}{4} ki te 2, ka \frac{3}{2}.

$$\frac{5}{2}-\frac{3}{2}x-4\times \left(\frac{2}{\sqrt{3}}\right)^{2}$$

Whakangāwaritia te tauraro o \frac{2}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{5}{2}-\frac{3}{2}x-4\times \left(\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5}{2}-\frac{3}{2}x-4\times \left(\frac{2\sqrt{3}}{3}\right)^{2}$$

Kia whakarewa i te \frac{2\sqrt{3}}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{5}{2}-\frac{3}{2}x-4\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}$$

Tuhia te 4\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}} hei hautanga kotahi.

$$\frac{5}{2}-\frac{3}{2}x-\frac{4\times \left(2\sqrt{3}\right)^{2}}{3^{2}}$$

Whakarohaina te \left(2\sqrt{3}\right)^{2}.

$$\frac{5}{2}-\frac{3}{2}x-\frac{4\times 2^{2}\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{5}{2}-\frac{3}{2}x-\frac{4\times 4\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5}{2}-\frac{3}{2}x-\frac{4\times 4\times 3}{3^{2}}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{5}{2}-\frac{3}{2}x-\frac{4\times 12}{3^{2}}$$

Whakareatia te 4 ki te 12, ka 48.

$$\frac{5}{2}-\frac{3}{2}x-\frac{48}{3^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\frac{5}{2}-\frac{3}{2}x-\frac{48}{9}$$

Whakahekea te hautanga \frac{48}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{5}{2}-\frac{3}{2}x-\frac{16}{3}$$

Tangohia te \frac{16}{3} i te \frac{5}{2}, ka -\frac{17}{6}.

$$-\frac{17}{6}-\frac{3}{2}x$$

Tauwehe

$$\frac{-9x-17}{6}$$

Ngā Upane Otinga

Ko te pūrua o \sqrt{3} ko 3.

$$factor(3-2\times \left(\frac{1}{2}\right)^{2}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2})$$

Tātaihia te \frac{1}{2} mā te pū o 2, kia riro ko \frac{1}{4}.

$$factor(3-2\times \frac{1}{4}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2})$$

Whakareatia te 2 ki te \frac{1}{4}, ka \frac{1}{2}.

$$factor(3-\frac{1}{2}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2})$$

Tangohia te \frac{1}{2} i te 3, ka \frac{5}{2}.

$$factor(\frac{5}{2}-\frac{3}{4}x\left(\sqrt{2}\right)^{2}-4\times \left(\frac{2}{\sqrt{3}}\right)^{2})$$

Ko te pūrua o \sqrt{2} ko 2.

$$factor(\frac{5}{2}-\frac{3}{4}x\times 2-4\times \left(\frac{2}{\sqrt{3}}\right)^{2})$$

Whakareatia te \frac{3}{4} ki te 2, ka \frac{3}{2}.

$$factor(\frac{5}{2}-\frac{3}{2}x-4\times \left(\frac{2}{\sqrt{3}}\right)^{2})$$

Whakangāwaritia te tauraro o \frac{2}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$factor(\frac{5}{2}-\frac{3}{2}x-4\times \left(\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2})$$

Ko te pūrua o \sqrt{3} ko 3.

$$factor(\frac{5}{2}-\frac{3}{2}x-4\times \left(\frac{2\sqrt{3}}{3}\right)^{2})$$

Kia whakarewa i te \frac{2\sqrt{3}}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$factor(\frac{5}{2}-\frac{3}{2}x-4\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}})$$

Tuhia te 4\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}} hei hautanga kotahi.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{4\times \left(2\sqrt{3}\right)^{2}}{3^{2}})$$

Whakarohaina te \left(2\sqrt{3}\right)^{2}.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{4\times 2^{2}\left(\sqrt{3}\right)^{2}}{3^{2}})$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{4\times 4\left(\sqrt{3}\right)^{2}}{3^{2}})$$

Ko te pūrua o \sqrt{3} ko 3.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{4\times 4\times 3}{3^{2}})$$

Whakareatia te 4 ki te 3, ka 12.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{4\times 12}{3^{2}})$$

Whakareatia te 4 ki te 12, ka 48.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{48}{3^{2}})$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{48}{9})$$

Whakahekea te hautanga \frac{48}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$factor(\frac{5}{2}-\frac{3}{2}x-\frac{16}{3})$$

Tangohia te \frac{16}{3} i te \frac{5}{2}, ka -\frac{17}{6}.

$$factor(-\frac{17}{6}-\frac{3}{2}x)$$

Tauwehea te \frac{1}{6}.

$$\frac{-17-9x}{6}$$