(x-1)^3(x+1)^3 eching

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

Baholash

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

Yechim qadamlari

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

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

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

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

x^{3}-3x^{2}+3x-1 ga x^{3}+3x^{2}+3x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{6}-3x^{4}+3x^{2}-1$$

Kengaytirish

$$x^{6}-3x^{4}+3x^{2}-1$$

Yechim qadamlari

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

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

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

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

x^{3}-3x^{2}+3x-1 ga x^{3}+3x^{2}+3x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{6}-3x^{4}+3x^{2}-1$$