Whakaoti i te (4sqrt{2}-3sqrt{6})(2sqrt{6}+3sqrt{2})

$$( 4 \sqrt { 2 } - 3 \sqrt { 6 } ) ( 2 \sqrt { 6 } + 3 \sqrt { 2 } )$$

Aromātai

$$-2\sqrt{3}-12\approx -15.464101615$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 4\sqrt{2}-3\sqrt{6} ki ia tau o 2\sqrt{6}+3\sqrt{2}.

$$8\sqrt{2}\sqrt{6}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$8\sqrt{2}\sqrt{2}\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$8\times 2\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Whakareatia te 8 ki te 2, ka 16.

$$16\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$16\sqrt{3}+12\times 2-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Whakareatia te 12 ki te 2, ka 24.

$$16\sqrt{3}+24-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Ko te pūrua o \sqrt{6} ko 6.

$$16\sqrt{3}+24-6\times 6-9\sqrt{6}\sqrt{2}$$

Whakareatia te -6 ki te 6, ka -36.

$$16\sqrt{3}+24-36-9\sqrt{6}\sqrt{2}$$

Tangohia te 36 i te 24, ka -12.

$$16\sqrt{3}-12-9\sqrt{6}\sqrt{2}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$16\sqrt{3}-12-9\sqrt{2}\sqrt{3}\sqrt{2}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$16\sqrt{3}-12-9\times 2\sqrt{3}$$

Whakareatia te -9 ki te 2, ka -18.

$$16\sqrt{3}-12-18\sqrt{3}$$

Pahekotia te 16\sqrt{3} me -18\sqrt{3}, ka -2\sqrt{3}.

$$-2\sqrt{3}-12$$

Tauwehe

$$2 {(-\sqrt{3} - 6)} = -15.464101615$$