(a-1)^2(a+2)+(1-a)(a+1)(a-2)= eching

$$( a - 1 ) ^ { 2 } ( a + 2 ) + ( 1 - a ) ( a + 1 ) ( a - 2 ) =$$

Baholash

$$2a\left(a-1\right)$$

Yechim qadamlari

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-1\right)^{2} kengaytirilishi uchun ishlating.

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

a^{2}-2a+1 ga a+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

1-a ga a+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

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

$$a^{3}-3a+2+a-2-a^{3}+2a^{2}$$

-2a ni olish uchun -3a va a ni birlashtirish.

$$a^{3}-2a+2-2-a^{3}+2a^{2}$$

0 olish uchun 2 dan 2 ni ayirish.

$$a^{3}-2a-a^{3}+2a^{2}$$

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

$$-2a+2a^{2}$$

Kengaytirish

$$2a^{2}-2a$$

Yechim qadamlari

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-1\right)^{2} kengaytirilishi uchun ishlating.

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

a^{2}-2a+1 ga a+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

1-a ga a+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

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

$$a^{3}-3a+2+a-2-a^{3}+2a^{2}$$

-2a ni olish uchun -3a va a ni birlashtirish.

$$a^{3}-2a+2-2-a^{3}+2a^{2}$$

0 olish uchun 2 dan 2 ni ayirish.

$$a^{3}-2a-a^{3}+2a^{2}$$

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

$$-2a+2a^{2}$$