left(9m^4/25-16n^4/9right)left(9m^4/25+16n^4/9right) eching

$$\left( \frac{ 9 { m }^{ 4 } }{ 25 } - \frac{ 16 { n }^{ 4 } }{ 9 } \right) \left( \frac{ 9 { m }^{ 4 } }{ 25 } + \frac{ 16 { n }^{ 4 } }{ 9 } \right)$$

Baholash

$$\frac{81m^{8}}{625}-\frac{256n^{8}}{81}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 25 va 9 ning eng kichik umumiy karralisi 225. \frac{9m^{4}}{25} ni \frac{9}{9} marotabaga ko'paytirish. \frac{16n^{4}}{9} ni \frac{25}{25} marotabaga ko'paytirish.

$$\left(\frac{9\times 9m^{4}}{225}-\frac{25\times 16n^{4}}{225}\right)\left(\frac{9m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

\frac{9\times 9m^{4}}{225} va \frac{25\times 16n^{4}}{225} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{9\times 9m^{4}-25\times 16n^{4}}{225}\left(\frac{9m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

9\times 9m^{4}-25\times 16n^{4} ichidagi ko‘paytirishlarni bajaring.

$$\frac{81m^{4}-400n^{4}}{225}\left(\frac{9m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 25 va 9 ning eng kichik umumiy karralisi 225. \frac{9m^{4}}{25} ni \frac{9}{9} marotabaga ko'paytirish. \frac{16n^{4}}{9} ni \frac{25}{25} marotabaga ko'paytirish.

$$\frac{81m^{4}-400n^{4}}{225}\left(\frac{9\times 9m^{4}}{225}+\frac{25\times 16n^{4}}{225}\right)$$

\frac{9\times 9m^{4}}{225} va \frac{25\times 16n^{4}}{225} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{81m^{4}-400n^{4}}{225}\times \frac{9\times 9m^{4}+25\times 16n^{4}}{225}$$

9\times 9m^{4}+25\times 16n^{4} ichidagi ko‘paytirishlarni bajaring.

$$\frac{81m^{4}-400n^{4}}{225}\times \frac{81m^{4}+400n^{4}}{225}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{81m^{4}-400n^{4}}{225} ni \frac{81m^{4}+400n^{4}}{225} ga ko‘paytiring.

$$\frac{\left(81m^{4}-400n^{4}\right)\left(81m^{4}+400n^{4}\right)}{225\times 225}$$

50625 hosil qilish uchun 225 va 225 ni ko'paytirish.

$$\frac{\left(81m^{4}-400n^{4}\right)\left(81m^{4}+400n^{4}\right)}{50625}$$

Hisoblang: \left(81m^{4}-400n^{4}\right)\left(81m^{4}+400n^{4}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(81m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

\left(81m^{4}\right)^{2} ni kengaytirish.

$$\frac{81^{2}\left(m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 2 ni ko‘paytirib, 8 ni oling.

$$\frac{81^{2}m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

2 daraja ko‘rsatkichini 81 ga hisoblang va 6561 ni qiymatni oling.

$$\frac{6561m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

\left(400n^{4}\right)^{2} ni kengaytirish.

$$\frac{6561m^{8}-400^{2}\left(n^{4}\right)^{2}}{50625}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 2 ni ko‘paytirib, 8 ni oling.

$$\frac{6561m^{8}-400^{2}n^{8}}{50625}$$

2 daraja ko‘rsatkichini 400 ga hisoblang va 160000 ni qiymatni oling.

$$\frac{6561m^{8}-160000n^{8}}{50625}$$

Kengaytirish

$$\frac{81m^{8}}{625}-\frac{256n^{8}}{81}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 25 va 9 ning eng kichik umumiy karralisi 225. \frac{9m^{4}}{25} ni \frac{9}{9} marotabaga ko'paytirish. \frac{16n^{4}}{9} ni \frac{25}{25} marotabaga ko'paytirish.

$$\left(\frac{9\times 9m^{4}}{225}-\frac{25\times 16n^{4}}{225}\right)\left(\frac{9m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

\frac{9\times 9m^{4}}{225} va \frac{25\times 16n^{4}}{225} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{9\times 9m^{4}-25\times 16n^{4}}{225}\left(\frac{9m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

9\times 9m^{4}-25\times 16n^{4} ichidagi ko‘paytirishlarni bajaring.

$$\frac{81m^{4}-400n^{4}}{225}\left(\frac{9m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 25 va 9 ning eng kichik umumiy karralisi 225. \frac{9m^{4}}{25} ni \frac{9}{9} marotabaga ko'paytirish. \frac{16n^{4}}{9} ni \frac{25}{25} marotabaga ko'paytirish.

$$\frac{81m^{4}-400n^{4}}{225}\left(\frac{9\times 9m^{4}}{225}+\frac{25\times 16n^{4}}{225}\right)$$

\frac{9\times 9m^{4}}{225} va \frac{25\times 16n^{4}}{225} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{81m^{4}-400n^{4}}{225}\times \frac{9\times 9m^{4}+25\times 16n^{4}}{225}$$

9\times 9m^{4}+25\times 16n^{4} ichidagi ko‘paytirishlarni bajaring.

$$\frac{81m^{4}-400n^{4}}{225}\times \frac{81m^{4}+400n^{4}}{225}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{81m^{4}-400n^{4}}{225} ni \frac{81m^{4}+400n^{4}}{225} ga ko‘paytiring.

$$\frac{\left(81m^{4}-400n^{4}\right)\left(81m^{4}+400n^{4}\right)}{225\times 225}$$

50625 hosil qilish uchun 225 va 225 ni ko'paytirish.

$$\frac{\left(81m^{4}-400n^{4}\right)\left(81m^{4}+400n^{4}\right)}{50625}$$

Hisoblang: \left(81m^{4}-400n^{4}\right)\left(81m^{4}+400n^{4}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(81m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

\left(81m^{4}\right)^{2} ni kengaytirish.

$$\frac{81^{2}\left(m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 2 ni ko‘paytirib, 8 ni oling.

$$\frac{81^{2}m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

2 daraja ko‘rsatkichini 81 ga hisoblang va 6561 ni qiymatni oling.

$$\frac{6561m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

\left(400n^{4}\right)^{2} ni kengaytirish.

$$\frac{6561m^{8}-400^{2}\left(n^{4}\right)^{2}}{50625}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 2 ni ko‘paytirib, 8 ni oling.

$$\frac{6561m^{8}-400^{2}n^{8}}{50625}$$

2 daraja ko‘rsatkichini 400 ga hisoblang va 160000 ni qiymatni oling.

$$\frac{6561m^{8}-160000n^{8}}{50625}$$