(1/2x^2-4x^-1)^3 eching

$$( \frac { 1 } { 2 } x ^ { 2 } - 4 x ^ { - 1 } ) ^ { 3 }$$

Baholash

$$\frac{\left(\frac{x^{3}-8}{x}\right)^{3}}{8}$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(\frac{1}{2}x^{2}-4x^{-1}\right)^{3} kengaytirilishi uchun ishlating.

$$\frac{1}{8}\left(x^{2}\right)^{3}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$\frac{1}{8}x^{6}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

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

$$\frac{1}{8}x^{6}-3x^{4}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va -1 ni qo‘shib, 3 ni oling.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -1 va 2 ni ko‘paytirib, -2 ni oling.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}x^{-2}-64\left(x^{-1}\right)^{3}$$

1 hosil qilish uchun x^{2} va x^{-2} ni ko'paytirish.

$$\frac{1}{8}x^{6}-3x^{3}+24-64\left(x^{-1}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -1 va 3 ni ko‘paytirib, -3 ni oling.

$$\frac{1}{8}x^{6}-3x^{3}+24-64x^{-3}$$

Kengaytirish

$$\frac{x^{6}}{8}-3x^{3}+24-\frac{64}{x^{3}}$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(\frac{1}{2}x^{2}-4x^{-1}\right)^{3} kengaytirilishi uchun ishlating.

$$\frac{1}{8}\left(x^{2}\right)^{3}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$\frac{1}{8}x^{6}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

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

$$\frac{1}{8}x^{6}-3x^{4}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va -1 ni qo‘shib, 3 ni oling.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -1 va 2 ni ko‘paytirib, -2 ni oling.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}x^{-2}-64\left(x^{-1}\right)^{3}$$

1 hosil qilish uchun x^{2} va x^{-2} ni ko'paytirish.

$$\frac{1}{8}x^{6}-3x^{3}+24-64\left(x^{-1}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -1 va 3 ni ko‘paytirib, -3 ni oling.

$$\frac{1}{8}x^{6}-3x^{3}+24-64x^{-3}$$