(x^2-10)^2-12(x^2-10)+32 eching

$$( x ^ { 2 } - 10 ) ^ { 2 } - 12 ( x ^ { 2 } - 10 ) + 32$$

Baholash

$$\left(x^{2}-18\right)\left(x^{2}-14\right)$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x^{2}-10\right)^{2} kengaytirilishi uchun ishlating.

$$\left(x^{2}\right)^{2}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

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

$$x^{4}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

-12 ga x^{2}-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{4}-20x^{2}+100-12x^{2}+120+32$$

-32x^{2} ni olish uchun -20x^{2} va -12x^{2} ni birlashtirish.

$$x^{4}-32x^{2}+100+120+32$$

220 olish uchun 100 va 120'ni qo'shing.

$$x^{4}-32x^{2}+220+32$$

252 olish uchun 220 va 32'ni qo'shing.

$$x^{4}-32x^{2}+252$$

Kengaytirish

$$x^{4}-32x^{2}+252$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x^{2}-10\right)^{2} kengaytirilishi uchun ishlating.

$$\left(x^{2}\right)^{2}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

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

$$x^{4}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

-12 ga x^{2}-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{4}-20x^{2}+100-12x^{2}+120+32$$

-32x^{2} ni olish uchun -20x^{2} va -12x^{2} ni birlashtirish.

$$x^{4}-32x^{2}+100+120+32$$

220 olish uchun 100 va 120'ni qo'shing.

$$x^{4}-32x^{2}+220+32$$

252 olish uchun 220 va 32'ni qo'shing.

$$x^{4}-32x^{2}+252$$