f(x)=-4(-4x^2+16)^3+5 eching

$$f ( x ) = - 4 ( - 4 x ^ { 2 } + 16 ) ^ { 3 } + 5$$

Baholash

$$-256\left(4-x^{2}\right)^{3}+5$$

Yechim qadamlari

\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} binom teoremasini \left(-4x^{2}+16\right)^{3} kengaytirilishi uchun ishlating.

$$-4\left(-64\left(x^{2}\right)^{3}+768\left(x^{2}\right)^{2}-3072x^{2}+4096\right)+5$$

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

$$-4\left(-64x^{6}+768\left(x^{2}\right)^{2}-3072x^{2}+4096\right)+5$$

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

$$-4\left(-64x^{6}+768x^{4}-3072x^{2}+4096\right)+5$$

-4 ga -64x^{6}+768x^{4}-3072x^{2}+4096 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$256x^{6}-3072x^{4}+12288x^{2}-16384+5$$

-16379 olish uchun -16384 va 5'ni qo'shing.

$$256x^{6}-3072x^{4}+12288x^{2}-16379$$

Kengaytirish

$$256x^{6}-3072x^{4}+12288x^{2}-16379$$

Yechim qadamlari

\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} binom teoremasini \left(-4x^{2}+16\right)^{3} kengaytirilishi uchun ishlating.

$$-4\left(-64\left(x^{2}\right)^{3}+768\left(x^{2}\right)^{2}-3072x^{2}+4096\right)+5$$

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

$$-4\left(-64x^{6}+768\left(x^{2}\right)^{2}-3072x^{2}+4096\right)+5$$

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

$$-4\left(-64x^{6}+768x^{4}-3072x^{2}+4096\right)+5$$

-4 ga -64x^{6}+768x^{4}-3072x^{2}+4096 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$256x^{6}-3072x^{4}+12288x^{2}-16384+5$$

-16379 olish uchun -16384 va 5'ni qo'shing.

$$256x^{6}-3072x^{4}+12288x^{2}-16379$$