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

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

Baholash

$$6x^{2}+2$$

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.

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

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

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

x^{3}-3x^{2}+3x-1 teskarisini topish uchun har birining teskarisini toping.

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

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

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

6x^{2} ni olish uchun 3x^{2} va 3x^{2} ni birlashtirish.

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

0 ni olish uchun 3x va -3x ni birlashtirish.

$$6x^{2}+1+1$$

2 olish uchun 1 va 1'ni qo'shing.

$$6x^{2}+2$$

Kengaytirish

$$6x^{2}+2$$

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.

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

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

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

x^{3}-3x^{2}+3x-1 teskarisini topish uchun har birining teskarisini toping.

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

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

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

6x^{2} ni olish uchun 3x^{2} va 3x^{2} ni birlashtirish.

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

0 ni olish uchun 3x va -3x ni birlashtirish.

$$6x^{2}+1+1$$

2 olish uchun 1 va 1'ni qo'shing.

$$6x^{2}+2$$