(x-1)^2+(x+2)^2-(x-3)(x+3)-22 eching

$$( x - 1 ) ^ { 2 } + ( x + 2 ) ^ { 2 } - ( x - 3 ) ( x + 3 ) - 22$$

Baholash

$$\left(x-2\right)\left(x+4\right)$$

Yechim qadamlari

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

$$x^{2}-2x+1+\left(x+2\right)^{2}-\left(x-3\right)\left(x+3\right)-22$$

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

$$x^{2}-2x+1+x^{2}+4x+4-\left(x-3\right)\left(x+3\right)-22$$

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

$$2x^{2}-2x+1+4x+4-\left(x-3\right)\left(x+3\right)-22$$

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

$$2x^{2}+2x+1+4-\left(x-3\right)\left(x+3\right)-22$$

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

$$2x^{2}+2x+5-\left(x-3\right)\left(x+3\right)-22$$

Hisoblang: \left(x-3\right)\left(x+3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$2x^{2}+2x+5-\left(x^{2}-9\right)-22$$

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

$$2x^{2}+2x+5-x^{2}+9-22$$

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

$$x^{2}+2x+5+9-22$$

14 olish uchun 5 va 9'ni qo'shing.

$$x^{2}+2x+14-22$$

-8 olish uchun 14 dan 22 ni ayirish.

$$x^{2}+2x-8$$

Kengaytirish

$$x^{2}+2x-8$$

Yechim qadamlari

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

$$x^{2}-2x+1+\left(x+2\right)^{2}-\left(x-3\right)\left(x+3\right)-22$$

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

$$x^{2}-2x+1+x^{2}+4x+4-\left(x-3\right)\left(x+3\right)-22$$

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

$$2x^{2}-2x+1+4x+4-\left(x-3\right)\left(x+3\right)-22$$

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

$$2x^{2}+2x+1+4-\left(x-3\right)\left(x+3\right)-22$$

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

$$2x^{2}+2x+5-\left(x-3\right)\left(x+3\right)-22$$

Hisoblang: \left(x-3\right)\left(x+3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$2x^{2}+2x+5-\left(x^{2}-9\right)-22$$

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

$$2x^{2}+2x+5-x^{2}+9-22$$

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

$$x^{2}+2x+5+9-22$$

14 olish uchun 5 va 9'ni qo'shing.

$$x^{2}+2x+14-22$$

-8 olish uchun 14 dan 22 ni ayirish.

$$x^{2}+2x-8$$