(y^{2}-x)^2+y^2(2x-y^2)-(-x-3)^2= eching

$$( y ^ { 2 } - x ) ^ { 2 } + y ^ { 2 } ( 2 x - y ^ { 2 } ) - ( - x - 3 ) ^ { 2 } =$$

Baholash

$$-6x-9$$

Yechim qadamlari

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

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

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

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

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

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

0 ni olish uchun -2y^{2}x va 2y^{2}x ni birlashtirish.

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

0 ni olish uchun y^{4} va -y^{4} ni birlashtirish.

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

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

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

2 daraja ko‘rsatkichini -x ga hisoblang va x^{2} ni qiymatni oling.

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

6 hosil qilish uchun -6 va -1 ni ko'paytirish.

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

x^{2}+6x+9 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-x^{2}-6x-9$$

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

$$-6x-9$$

Kengaytirish

$$-6x-9$$

Yechim qadamlari

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

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

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

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

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

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

0 ni olish uchun -2y^{2}x va 2y^{2}x ni birlashtirish.

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

0 ni olish uchun y^{4} va -y^{4} ni birlashtirish.

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

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

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

2 daraja ko‘rsatkichini -x ga hisoblang va x^{2} ni qiymatni oling.

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

6 hosil qilish uchun -6 va -1 ni ko'paytirish.

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

x^{2}+6x+9 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-x^{2}-6x-9$$

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

$$-6x-9$$