Whakaoti i te (3sqrt{2}-6sqrt{5})(5sqrt{2}+10sqrt{5})

$$( 3 \sqrt { 2 } - 6 \sqrt { 5 } ) ( 5 \sqrt { 2 } + 10 \sqrt { 5 } )$$

Aromātai

$$-270$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3\sqrt{2}-6\sqrt{5} ki ia tau o 5\sqrt{2}+10\sqrt{5}.

$$15\left(\sqrt{2}\right)^{2}+30\sqrt{2}\sqrt{5}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$15\times 2+30\sqrt{2}\sqrt{5}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

Whakareatia te 15 ki te 2, ka 30.

$$30+30\sqrt{2}\sqrt{5}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$30+30\sqrt{10}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

Hei whakarea \sqrt{5} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$30+30\sqrt{10}-30\sqrt{10}-60\left(\sqrt{5}\right)^{2}$$

Pahekotia te 30\sqrt{10} me -30\sqrt{10}, ka 0.

$$30-60\left(\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{5} ko 5.

$$30-60\times 5$$

Whakareatia te -60 ki te 5, ka -300.

$$30-300$$

Tangohia te 300 i te 30, ka -270.

$$-270$$

Tauwehe

$$-270$$