(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

$$x^{3}-27x^{2}+263x-837$$

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.

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

81 olish uchun 49 va 32'ni qo'shing.

$$\left(x-13\right)\left(x^{2}-14x+81\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

x-13 ifodaning har bir elementini x^{2}-14x+81 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$x^{3}-14x^{2}+81x-13x^{2}+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+81x+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

263x ni olish uchun 81x va 182x ni birlashtirish.

$$x^{3}-27x^{2}+263x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+263x-1053-10x+270+2\left(8+5\left(x-7\right)\right)$$

253x ni olish uchun 263x va -10x ni birlashtirish.

$$x^{3}-27x^{2}+253x-1053+270+2\left(8+5\left(x-7\right)\right)$$

-783 olish uchun -1053 va 270'ni qo'shing.

$$x^{3}-27x^{2}+253x-783+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+253x-783+2\left(8+5x-35\right)$$

-27 olish uchun 8 dan 35 ni ayirish.

$$x^{3}-27x^{2}+253x-783+2\left(-27+5x\right)$$

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

$$x^{3}-27x^{2}+253x-783-54+10x$$

-837 olish uchun -783 dan 54 ni ayirish.

$$x^{3}-27x^{2}+253x-837+10x$$

263x ni olish uchun 253x va 10x ni birlashtirish.

$$x^{3}-27x^{2}+263x-837$$

Kengaytirish

$$x^{3}-27x^{2}+263x-837$$

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.

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

81 olish uchun 49 va 32'ni qo'shing.

$$\left(x-13\right)\left(x^{2}-14x+81\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

x-13 ifodaning har bir elementini x^{2}-14x+81 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$x^{3}-14x^{2}+81x-13x^{2}+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+81x+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

263x ni olish uchun 81x va 182x ni birlashtirish.

$$x^{3}-27x^{2}+263x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+263x-1053-10x+270+2\left(8+5\left(x-7\right)\right)$$

253x ni olish uchun 263x va -10x ni birlashtirish.

$$x^{3}-27x^{2}+253x-1053+270+2\left(8+5\left(x-7\right)\right)$$

-783 olish uchun -1053 va 270'ni qo'shing.

$$x^{3}-27x^{2}+253x-783+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+253x-783+2\left(8+5x-35\right)$$

-27 olish uchun 8 dan 35 ni ayirish.

$$x^{3}-27x^{2}+253x-783+2\left(-27+5x\right)$$

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

$$x^{3}-27x^{2}+253x-783-54+10x$$

-837 olish uchun -783 dan 54 ni ayirish.

$$x^{3}-27x^{2}+253x-837+10x$$

263x ni olish uchun 253x va 10x ni birlashtirish.

$$x^{3}-27x^{2}+263x-837$$