(x^2-2)^2-4(x^2-2)+4 eching

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

Baholash

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

Yechim qadamlari

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

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

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

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

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

$$x^{4}-4x^{2}+4-4x^{2}+8+4$$

-8x^{2} ni olish uchun -4x^{2} va -4x^{2} ni birlashtirish.

$$x^{4}-8x^{2}+4+8+4$$

12 olish uchun 4 va 8'ni qo'shing.

$$x^{4}-8x^{2}+12+4$$

16 olish uchun 12 va 4'ni qo'shing.

$$x^{4}-8x^{2}+16$$

Kengaytirish

$$x^{4}-8x^{2}+16$$

Yechim qadamlari

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

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

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

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

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

$$x^{4}-4x^{2}+4-4x^{2}+8+4$$

-8x^{2} ni olish uchun -4x^{2} va -4x^{2} ni birlashtirish.

$$x^{4}-8x^{2}+4+8+4$$

12 olish uchun 4 va 8'ni qo'shing.

$$x^{4}-8x^{2}+12+4$$

16 olish uchun 12 va 4'ni qo'shing.

$$x^{4}-8x^{2}+16$$