(x-13)((x-7)(x-7)-32)+5(-2(x-7)+40)+2(8+5(x-7)) eching

$$( x - 13 ) ( ( x - 7 ) ( x - 7 ) - 32 ) + 5 ( - 2 ( x - 7 ) + 40 ) + 2 ( 8 + 5 ( x - 7 ) )$$

Baholash

$$x^{3}-27x^{2}+199x-5$$

Yechim qadamlari

\left(x-7\right)^{2} hosil qilish uchun x-7 va x-7 ni ko'paytirish.

$$\left(x-13\right)\left(\left(x-7\right)^{2}-32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-7\right)^{2} kengaytirilishi uchun ishlating.

$$\left(x-13\right)\left(x^{2}-14x+49-32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

17 olish uchun 49 dan 32 ni ayirish.

$$\left(x-13\right)\left(x^{2}-14x+17\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

x-13 ifodaning har bir elementini x^{2}-14x+17 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$x^{3}-14x^{2}+17x-13x^{2}+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

-27x^{2} ni olish uchun -14x^{2} va -13x^{2} ni birlashtirish.

$$x^{3}-27x^{2}+17x+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

199x ni olish uchun 17x va 182x ni birlashtirish.

$$x^{3}-27x^{2}+199x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

-2 ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+199x-221+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

54 olish uchun 14 va 40'ni qo'shing.

$$x^{3}-27x^{2}+199x-221+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

5 ga -2x+54 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+199x-221-10x+270+2\left(8+5\left(x-7\right)\right)$$

189x ni olish uchun 199x va -10x ni birlashtirish.

$$x^{3}-27x^{2}+189x-221+270+2\left(8+5\left(x-7\right)\right)$$

49 olish uchun -221 va 270'ni qo'shing.

$$x^{3}-27x^{2}+189x+49+2\left(8+5\left(x-7\right)\right)$$

5 ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+189x+49+2\left(8+5x-35\right)$$

-27 olish uchun 8 dan 35 ni ayirish.

$$x^{3}-27x^{2}+189x+49+2\left(-27+5x\right)$$

2 ga -27+5x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+189x+49-54+10x$$

-5 olish uchun 49 dan 54 ni ayirish.

$$x^{3}-27x^{2}+189x-5+10x$$

199x ni olish uchun 189x va 10x ni birlashtirish.

$$x^{3}-27x^{2}+199x-5$$

Kengaytirish

$$x^{3}-27x^{2}+199x-5$$

Yechim qadamlari

\left(x-7\right)^{2} hosil qilish uchun x-7 va x-7 ni ko'paytirish.

$$\left(x-13\right)\left(\left(x-7\right)^{2}-32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-7\right)^{2} kengaytirilishi uchun ishlating.

$$\left(x-13\right)\left(x^{2}-14x+49-32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

17 olish uchun 49 dan 32 ni ayirish.

$$\left(x-13\right)\left(x^{2}-14x+17\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

x-13 ifodaning har bir elementini x^{2}-14x+17 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$x^{3}-14x^{2}+17x-13x^{2}+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

-27x^{2} ni olish uchun -14x^{2} va -13x^{2} ni birlashtirish.

$$x^{3}-27x^{2}+17x+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

199x ni olish uchun 17x va 182x ni birlashtirish.

$$x^{3}-27x^{2}+199x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

-2 ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+199x-221+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

54 olish uchun 14 va 40'ni qo'shing.

$$x^{3}-27x^{2}+199x-221+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

5 ga -2x+54 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+199x-221-10x+270+2\left(8+5\left(x-7\right)\right)$$

189x ni olish uchun 199x va -10x ni birlashtirish.

$$x^{3}-27x^{2}+189x-221+270+2\left(8+5\left(x-7\right)\right)$$

49 olish uchun -221 va 270'ni qo'shing.

$$x^{3}-27x^{2}+189x+49+2\left(8+5\left(x-7\right)\right)$$

5 ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+189x+49+2\left(8+5x-35\right)$$

-27 olish uchun 8 dan 35 ni ayirish.

$$x^{3}-27x^{2}+189x+49+2\left(-27+5x\right)$$

2 ga -27+5x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{3}-27x^{2}+189x+49-54+10x$$

-5 olish uchun 49 dan 54 ni ayirish.

$$x^{3}-27x^{2}+189x-5+10x$$

199x ni olish uchun 189x va 10x ni birlashtirish.

$$x^{3}-27x^{2}+199x-5$$