(x^2+1)^2-7(x^2+1)+10 eching

$$( x ^ { 2 } + 1 ) ^ { 2 } - 7 ( x ^ { 2 } + 1 ) + 10$$

Baholash

$$x^{4}-5x^{2}+4$$

Yechim qadamlari

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

$$\left(x^{2}\right)^{2}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

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

$$x^{4}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

-7 ga x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{4}+2x^{2}+1-7x^{2}-7+10$$

-5x^{2} ni olish uchun 2x^{2} va -7x^{2} ni birlashtirish.

$$x^{4}-5x^{2}+1-7+10$$

-6 olish uchun 1 dan 7 ni ayirish.

$$x^{4}-5x^{2}-6+10$$

4 olish uchun -6 va 10'ni qo'shing.

$$x^{4}-5x^{2}+4$$

Kengaytirish

$$x^{4}-5x^{2}+4$$

Yechim qadamlari

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

$$\left(x^{2}\right)^{2}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

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

$$x^{4}+2x^{2}+1-7\left(x^{2}+1\right)+10$$

-7 ga x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{4}+2x^{2}+1-7x^{2}-7+10$$

-5x^{2} ni olish uchun 2x^{2} va -7x^{2} ni birlashtirish.

$$x^{4}-5x^{2}+1-7+10$$

-6 olish uchun 1 dan 7 ni ayirish.

$$x^{4}-5x^{2}-6+10$$

4 olish uchun -6 va 10'ni qo'shing.

$$x^{4}-5x^{2}+4$$