(x-2)^2-(2x-1)(2x+1) eching

$$( x - 2 ) ^ { 2 } - ( 2 x - 1 ) ( 2 x + 1 )$$

Baholash

$$5-4x-3x^{2}$$

Yechim qadamlari

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

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

Hisoblang: \left(2x-1\right)\left(2x+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.

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

\left(2x\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

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

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

$$x^{2}-4x+4-4x^{2}+1$$

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$-3x^{2}-4x+4+1$$

5 olish uchun 4 va 1'ni qo'shing.

$$-3x^{2}-4x+5$$

Kengaytirish

$$5-4x-3x^{2}$$

Yechim qadamlari

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

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

Hisoblang: \left(2x-1\right)\left(2x+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.

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

\left(2x\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

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

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

$$x^{2}-4x+4-4x^{2}+1$$

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$-3x^{2}-4x+4+1$$

5 olish uchun 4 va 1'ni qo'shing.

$$-3x^{2}-4x+5$$