Whakaoti i te (2sqrt{7}-5)^2*(2sqrt{7}+5)^2

$$( 2 \sqrt { 7 } - 5 ) ^ { 2 } \cdot ( 2 \sqrt { 7 } + 5 ) ^ { 2 }$$

Aromātai

$$9$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2\sqrt{7}-5\right)^{2}.

$$\left(4\left(\sqrt{7}\right)^{2}-20\sqrt{7}+25\right)\left(2\sqrt{7}+5\right)^{2}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\left(4\times 7-20\sqrt{7}+25\right)\left(2\sqrt{7}+5\right)^{2}$$

Whakareatia te 4 ki te 7, ka 28.

$$\left(28-20\sqrt{7}+25\right)\left(2\sqrt{7}+5\right)^{2}$$

Tāpirihia te 28 ki te 25, ka 53.

$$\left(53-20\sqrt{7}\right)\left(2\sqrt{7}+5\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2\sqrt{7}+5\right)^{2}.

$$\left(53-20\sqrt{7}\right)\left(4\left(\sqrt{7}\right)^{2}+20\sqrt{7}+25\right)$$

Ko te pūrua o \sqrt{7} ko 7.

$$\left(53-20\sqrt{7}\right)\left(4\times 7+20\sqrt{7}+25\right)$$

Whakareatia te 4 ki te 7, ka 28.

$$\left(53-20\sqrt{7}\right)\left(28+20\sqrt{7}+25\right)$$

Tāpirihia te 28 ki te 25, ka 53.

$$\left(53-20\sqrt{7}\right)\left(53+20\sqrt{7}\right)$$

Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 53.

$$2809-\left(20\sqrt{7}\right)^{2}$$

Whakarohaina te \left(20\sqrt{7}\right)^{2}.

$$2809-20^{2}\left(\sqrt{7}\right)^{2}$$

Tātaihia te 20 mā te pū o 2, kia riro ko 400.

$$2809-400\left(\sqrt{7}\right)^{2}$$

Ko te pūrua o \sqrt{7} ko 7.

$$2809-400\times 7$$

Whakareatia te 400 ki te 7, ka 2800.

$$2809-2800$$

Tangohia te 2800 i te 2809, ka 9.

$$9$$

Tauwehe

$$3^{2}$$