f(x)=-2(x^2+1)^2(x^2+1)(x-1) eching

$$f ( x ) = - 2 ( x ^ { 2 } + 1 ) ^ { 2 } ( x ^ { 2 } + 1 ) ( x - 1 )$$

Baholash

$$-2\left(x-1\right)\left(x^{2}+1\right)^{3}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$-2\left(x^{2}+1\right)^{3}\left(x-1\right)$$

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

$$-2\left(\left(x^{2}\right)^{3}+3\left(x^{2}\right)^{2}+3x^{2}+1\right)\left(x-1\right)$$

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

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

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

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

-2 ga x^{6}+3x^{4}+3x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-2x^{6}-6x^{4}-6x^{2}-2\right)\left(x-1\right)$$

-2x^{6}-6x^{4}-6x^{2}-2 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2x^{7}+2x^{6}-6x^{5}+6x^{4}-6x^{3}+6x^{2}-2x+2$$

Kengaytirish

$$2-2x+6x^{2}-6x^{3}+6x^{4}-6x^{5}+2x^{6}-2x^{7}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$-2\left(x^{2}+1\right)^{3}\left(x-1\right)$$

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

$$-2\left(\left(x^{2}\right)^{3}+3\left(x^{2}\right)^{2}+3x^{2}+1\right)\left(x-1\right)$$

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

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

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

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

-2 ga x^{6}+3x^{4}+3x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-2x^{6}-6x^{4}-6x^{2}-2\right)\left(x-1\right)$$

-2x^{6}-6x^{4}-6x^{2}-2 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2x^{7}+2x^{6}-6x^{5}+6x^{4}-6x^{3}+6x^{2}-2x+2$$