(x^2-3)^2-x(x^2-3)-2x^2 eching

$$( x ^ { 2 } - 3 ) ^ { 2 } - x ( x ^ { 2 } - 3 ) - 2 x ^ { 2 }$$

Baholash

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

Yechim qadamlari

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

$$\left(x^{2}\right)^{2}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

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

$$x^{4}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

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

$$x^{4}-6x^{2}+9-\left(x^{3}-3x\right)-2x^{2}$$

x^{3}-3x teskarisini topish uchun har birining teskarisini toping.

$$x^{4}-6x^{2}+9-x^{3}+3x-2x^{2}$$

-8x^{2} ni olish uchun -6x^{2} va -2x^{2} ni birlashtirish.

$$x^{4}-8x^{2}+9-x^{3}+3x$$

Kengaytirish

$$x^{4}-x^{3}-8x^{2}+3x+9$$

Yechim qadamlari

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

$$\left(x^{2}\right)^{2}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

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

$$x^{4}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

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

$$x^{4}-6x^{2}+9-\left(x^{3}-3x\right)-2x^{2}$$

x^{3}-3x teskarisini topish uchun har birining teskarisini toping.

$$x^{4}-6x^{2}+9-x^{3}+3x-2x^{2}$$

-8x^{2} ni olish uchun -6x^{2} va -2x^{2} ni birlashtirish.

$$x^{4}-8x^{2}+9-x^{3}+3x$$