[(x+1)(x-1)]^2-(2+x^2)^2+3/2(2x-3)(2x+3) eching

$$[ ( x + 1 ) ( x - 1 ) ] ^ { 2 } - ( 2 + x ^ { 2 } ) ^ { 2 } + \frac { 3 } { 2 } ( 2 x - 3 ) ( 2 x + 3 )$$

Baholash

$$-\frac{33}{2}=-16,5$$

Yechim qadamlari

Hisoblang: \left(x+1\right)\left(x-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

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

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

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

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

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

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

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

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

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

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

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

-3 olish uchun 1 dan 4 ni ayirish.

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

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

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

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

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

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

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

3x-\frac{9}{2} ga 2x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-6x^{2}-3+6x^{2}-\frac{27}{2}$$

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

$$-3-\frac{27}{2}$$

-\frac{33}{2} olish uchun -3 dan \frac{27}{2} ni ayirish.

$$-\frac{33}{2}$$

Omil

$$-\frac{33}{2} = -16\frac{1}{2} = -16,5$$

Yechim qadamlari

\frac{1}{2} omili.

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

Qisqartirish.

$$-\frac{33}{2}$$