[(x+1)^{2}-4x]^{2}-(x^2+1)^2-(x^2-2x)^2 eching

$$[ ( x + 1 ) ^ { 2 } - 4 x ] ^ { 2 } - ( x ^ { 2 } + 1 ) ^ { 2 } - ( x ^ { 2 } - 2 x ) ^ { 2 }$$

Baholash

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

Yechim qadamlari

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

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

-2x ni olish uchun 2x va -4x ni birlashtirish.

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

x^{2}-2x+1 kvadratini chiqarish.

$$x^{4}-4x^{3}+6x^{2}-4x+1-\left(x^{2}+1\right)^{2}-\left(x^{2}-2x\right)^{2}$$

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

$$x^{4}-4x^{3}+6x^{2}-4x+1-\left(\left(x^{2}\right)^{2}+2x^{2}+1\right)-\left(x^{2}-2x\right)^{2}$$

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

$$x^{4}-4x^{3}+6x^{2}-4x+1-\left(x^{4}+2x^{2}+1\right)-\left(x^{2}-2x\right)^{2}$$

x^{4}+2x^{2}+1 teskarisini topish uchun har birining teskarisini toping.

$$x^{4}-4x^{3}+6x^{2}-4x+1-x^{4}-2x^{2}-1-\left(x^{2}-2x\right)^{2}$$

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

$$-4x^{3}+6x^{2}-4x+1-2x^{2}-1-\left(x^{2}-2x\right)^{2}$$

4x^{2} ni olish uchun 6x^{2} va -2x^{2} ni birlashtirish.

$$-4x^{3}+4x^{2}-4x+1-1-\left(x^{2}-2x\right)^{2}$$

0 olish uchun 1 dan 1 ni ayirish.

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

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

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

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

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

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

x^{4}-4x^{3}+4x^{2} teskarisini topish uchun har birining teskarisini toping.

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

0 ni olish uchun -4x^{3} va 4x^{3} ni birlashtirish.

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

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

$$-4x-x^{4}$$

Kengaytirish

$$-x^{4}-4x$$

Yechim qadamlari

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

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

-2x ni olish uchun 2x va -4x ni birlashtirish.

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

x^{2}-2x+1 kvadratini chiqarish.

$$x^{4}-4x^{3}+6x^{2}-4x+1-\left(x^{2}+1\right)^{2}-\left(x^{2}-2x\right)^{2}$$

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

$$x^{4}-4x^{3}+6x^{2}-4x+1-\left(\left(x^{2}\right)^{2}+2x^{2}+1\right)-\left(x^{2}-2x\right)^{2}$$

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

$$x^{4}-4x^{3}+6x^{2}-4x+1-\left(x^{4}+2x^{2}+1\right)-\left(x^{2}-2x\right)^{2}$$

x^{4}+2x^{2}+1 teskarisini topish uchun har birining teskarisini toping.

$$x^{4}-4x^{3}+6x^{2}-4x+1-x^{4}-2x^{2}-1-\left(x^{2}-2x\right)^{2}$$

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

$$-4x^{3}+6x^{2}-4x+1-2x^{2}-1-\left(x^{2}-2x\right)^{2}$$

4x^{2} ni olish uchun 6x^{2} va -2x^{2} ni birlashtirish.

$$-4x^{3}+4x^{2}-4x+1-1-\left(x^{2}-2x\right)^{2}$$

0 olish uchun 1 dan 1 ni ayirish.

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

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

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

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

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

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

x^{4}-4x^{3}+4x^{2} teskarisini topish uchun har birining teskarisini toping.

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

0 ni olish uchun -4x^{3} va 4x^{3} ni birlashtirish.

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

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

$$-4x-x^{4}$$