(4-x^{2})^2(x^3-2)+x^3(-x^4-2)+32 eching

$$( 4 - x ^ { 2 } ) ^ { 2 } ( x ^ { 3 } - 2 ) + x ^ { 3 } ( - x ^ { 4 } - 2 ) + 32$$

Baholash

$$2x^{2}\left(8+7x-x^{2}-4x^{3}\right)$$

Yechim qadamlari

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

$$\left(16-8x^{2}+\left(x^{2}\right)^{2}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

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

$$\left(16-8x^{2}+x^{4}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

16-8x^{2}+x^{4} ga x^{3}-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}-2\right)+32$$

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

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)-2x^{3}+32$$

14x^{3} ni olish uchun 16x^{3} va -2x^{3} ni birlashtirish.

$$14x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)+32$$

0 olish uchun -32 va 32'ni qo'shing.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 4 ni qo‘shib, 7 ni oling.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{7}\left(-1\right)$$

0 ni olish uchun x^{7} va x^{7}\left(-1\right) ni birlashtirish.

$$14x^{3}-8x^{5}+16x^{2}-2x^{4}$$

Kengaytirish

$$16x^{2}+14x^{3}-2x^{4}-8x^{5}$$

Yechim qadamlari

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

$$\left(16-8x^{2}+\left(x^{2}\right)^{2}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

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

$$\left(16-8x^{2}+x^{4}\right)\left(x^{3}-2\right)+x^{3}\left(-x^{4}-2\right)+32$$

16-8x^{2}+x^{4} ga x^{3}-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}-2\right)+32$$

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

$$16x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)-2x^{3}+32$$

14x^{3} ni olish uchun 16x^{3} va -2x^{3} ni birlashtirish.

$$14x^{3}-32-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)+32$$

0 olish uchun -32 va 32'ni qo'shing.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{3}\left(-x^{4}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 4 ni qo‘shib, 7 ni oling.

$$14x^{3}-8x^{5}+16x^{2}+x^{7}-2x^{4}+x^{7}\left(-1\right)$$

0 ni olish uchun x^{7} va x^{7}\left(-1\right) ni birlashtirish.

$$14x^{3}-8x^{5}+16x^{2}-2x^{4}$$