(x^{2}+1)^{3}-(x^{3}+1)^2+3x^2(x+1)(x-1)-(-3x^2)(-2x^2)= eching

$$( x ^ { 2 } + 1 ) ^ { 3 } - ( x ^ { 3 } + 1 ) ^ { 2 } + 3 x ^ { 2 } ( x + 1 ) ( x - 1 ) - ( - 3 x ^ { 2 } ) ( - 2 x ^ { 2 } ) =$$

Baholash

$$-2x^{3}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 2 ni qo‘shib, 4 ni oling.

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

\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.

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

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

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

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

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

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

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

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

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

x^{6}+2x^{3}+1 teskarisini topish uchun har birining teskarisini toping.

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

0 ni olish uchun x^{6} va -x^{6} ni birlashtirish.

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

0 olish uchun 1 dan 1 ni ayirish.

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

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

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

3x^{3}+3x^{2} ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

6x^{4} ni olish uchun 3x^{4} va 3x^{4} ni birlashtirish.

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

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

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

6 hosil qilish uchun -3 va -2 ni ko'paytirish.

$$6x^{4}-2x^{3}-6x^{4}$$

0 ni olish uchun 6x^{4} va -6x^{4} ni birlashtirish.

$$-2x^{3}$$

Kengaytirish

$$-2x^{3}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 2 ni qo‘shib, 4 ni oling.

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

\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.

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

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

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

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

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

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

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

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

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

x^{6}+2x^{3}+1 teskarisini topish uchun har birining teskarisini toping.

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

0 ni olish uchun x^{6} va -x^{6} ni birlashtirish.

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

0 olish uchun 1 dan 1 ni ayirish.

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

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

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

3x^{3}+3x^{2} ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

6x^{4} ni olish uchun 3x^{4} va 3x^{4} ni birlashtirish.

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

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

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

6 hosil qilish uchun -3 va -2 ni ko'paytirish.

$$6x^{4}-2x^{3}-6x^{4}$$

0 ni olish uchun 6x^{4} va -6x^{4} ni birlashtirish.

$$-2x^{3}$$