1/2x(3-x)+3(x+1)(x-1)-x(x-1)^2+(x-1)^3-1/2(2x-8) eching

$$\frac { 1 } { 2 } x ( 3 - x ) + 3 ( x + 1 ) ( x - 1 ) - x ( x - 1 ) ^ { 2 } + ( x - 1 ) ^ { 3 } - \frac { 1 } { 2 } ( 2 x - 8 )$$

Baholash

$$\frac{x\left(3x+5\right)}{2}$$

Yechim qadamlari

\frac{1}{2}x ga 3-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}x-\frac{1}{2}x^{2}+3\left(x+1\right)\left(x-1\right)-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

3 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}x-\frac{1}{2}x^{2}+\left(3x+3\right)\left(x-1\right)-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

3x+3 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{3}{2}x-\frac{1}{2}x^{2}+3x^{2}-3-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\frac{5}{2}x^{2} ni olish uchun -\frac{1}{2}x^{2} va 3x^{2} ni birlashtirish.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x^{2}-2x+1\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-\left(x^{3}-2x^{2}+x\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x^{3}+2x^{2}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\frac{9}{2}x^{2} ni olish uchun \frac{5}{2}x^{2} va 2x^{2} ni birlashtirish.

$$\frac{3}{2}x+\frac{9}{2}x^{2}-3-x^{3}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\frac{1}{2}x ni olish uchun \frac{3}{2}x va -x ni birlashtirish.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(x-1\right)^{3} kengaytirilishi uchun ishlating.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+x^{3}-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

\frac{3}{2}x^{2} ni olish uchun \frac{9}{2}x^{2} va -3x^{2} ni birlashtirish.

$$\frac{1}{2}x+\frac{3}{2}x^{2}-3+3x-1-\frac{1}{2}\left(2x-8\right)$$

\frac{7}{2}x ni olish uchun \frac{1}{2}x va 3x ni birlashtirish.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-3-1-\frac{1}{2}\left(2x-8\right)$$

-4 olish uchun -3 dan 1 ni ayirish.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-4-\frac{1}{2}\left(2x-8\right)$$

-\frac{1}{2} ga 2x-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-4-x+4$$

\frac{5}{2}x ni olish uchun \frac{7}{2}x va -x ni birlashtirish.

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

0 olish uchun -4 va 4'ni qo'shing.

$$\frac{5}{2}x+\frac{3}{2}x^{2}$$

Kengaytirish

$$\frac{3x^{2}+5x}{2}$$

Yechim qadamlari

\frac{1}{2}x ga 3-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}x-\frac{1}{2}x^{2}+3\left(x+1\right)\left(x-1\right)-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

3 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}x-\frac{1}{2}x^{2}+\left(3x+3\right)\left(x-1\right)-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

3x+3 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{3}{2}x-\frac{1}{2}x^{2}+3x^{2}-3-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\frac{5}{2}x^{2} ni olish uchun -\frac{1}{2}x^{2} va 3x^{2} ni birlashtirish.

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x-1\right)^{2}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x\left(x^{2}-2x+1\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-\left(x^{3}-2x^{2}+x\right)+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{3}{2}x+\frac{5}{2}x^{2}-3-x^{3}+2x^{2}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\frac{9}{2}x^{2} ni olish uchun \frac{5}{2}x^{2} va 2x^{2} ni birlashtirish.

$$\frac{3}{2}x+\frac{9}{2}x^{2}-3-x^{3}-x+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\frac{1}{2}x ni olish uchun \frac{3}{2}x va -x ni birlashtirish.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+\left(x-1\right)^{3}-\frac{1}{2}\left(2x-8\right)$$

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(x-1\right)^{3} kengaytirilishi uchun ishlating.

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-x^{3}+x^{3}-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

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

$$\frac{1}{2}x+\frac{9}{2}x^{2}-3-3x^{2}+3x-1-\frac{1}{2}\left(2x-8\right)$$

\frac{3}{2}x^{2} ni olish uchun \frac{9}{2}x^{2} va -3x^{2} ni birlashtirish.

$$\frac{1}{2}x+\frac{3}{2}x^{2}-3+3x-1-\frac{1}{2}\left(2x-8\right)$$

\frac{7}{2}x ni olish uchun \frac{1}{2}x va 3x ni birlashtirish.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-3-1-\frac{1}{2}\left(2x-8\right)$$

-4 olish uchun -3 dan 1 ni ayirish.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-4-\frac{1}{2}\left(2x-8\right)$$

-\frac{1}{2} ga 2x-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{7}{2}x+\frac{3}{2}x^{2}-4-x+4$$

\frac{5}{2}x ni olish uchun \frac{7}{2}x va -x ni birlashtirish.

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

0 olish uchun -4 va 4'ni qo'shing.

$$\frac{5}{2}x+\frac{3}{2}x^{2}$$