(x-a)(x^{2}+ax+a^2)-a^2x-(x+a)(x-a)(x-1)+a^2(a-3)+(2a-x)^2 eching

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

Baholash

$$2x\left(x-2a\right)$$

Yechim qadamlari

x-a ga x^{2}+ax+a^{2} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x+a ga x-a ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x^{2}-a^{2} ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

a^{2} ga a-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Kengaytirish

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

Yechim qadamlari

x-a ga x^{2}+ax+a^{2} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x+a ga x-a ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x^{2}-a^{2} ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

a^{2} ga a-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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