4(m+n)^2-4(m+n)(n-2)+(n-2)^2 eching

$$4 ( m + n ) ^ { 2 } - 4 ( m + n ) ( n - 2 ) + ( n - 2 ) ^ { 2 }$$

Baholash

$$\left(2m+n+2\right)^{2}$$

Yechim qadamlari

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

$$4\left(m^{2}+2mn+n^{2}\right)-4\left(m+n\right)\left(n-2\right)+\left(n-2\right)^{2}$$

4 ga m^{2}+2mn+n^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+\left(n-2\right)^{2}$$

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

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+n^{2}-4n+4$$

-4 ga m+n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}+8mn+4n^{2}+\left(-4m-4n\right)\left(n-2\right)+n^{2}-4n+4$$

-4m-4n ga n-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}+8mn+4n^{2}-4mn+8m-4n^{2}+8n+n^{2}-4n+4$$

4mn ni olish uchun 8mn va -4mn ni birlashtirish.

$$4m^{2}+4mn+4n^{2}+8m-4n^{2}+8n+n^{2}-4n+4$$

0 ni olish uchun 4n^{2} va -4n^{2} ni birlashtirish.

$$4m^{2}+4mn+8m+8n+n^{2}-4n+4$$

4n ni olish uchun 8n va -4n ni birlashtirish.

$$4m^{2}+4mn+8m+4n+n^{2}+4$$

Kengaytirish

$$4m^{2}+4mn+8m+n^{2}+4n+4$$

Yechim qadamlari

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

$$4\left(m^{2}+2mn+n^{2}\right)-4\left(m+n\right)\left(n-2\right)+\left(n-2\right)^{2}$$

4 ga m^{2}+2mn+n^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+\left(n-2\right)^{2}$$

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

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+n^{2}-4n+4$$

-4 ga m+n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}+8mn+4n^{2}+\left(-4m-4n\right)\left(n-2\right)+n^{2}-4n+4$$

-4m-4n ga n-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}+8mn+4n^{2}-4mn+8m-4n^{2}+8n+n^{2}-4n+4$$

4mn ni olish uchun 8mn va -4mn ni birlashtirish.

$$4m^{2}+4mn+4n^{2}+8m-4n^{2}+8n+n^{2}-4n+4$$

0 ni olish uchun 4n^{2} va -4n^{2} ni birlashtirish.

$$4m^{2}+4mn+8m+8n+n^{2}-4n+4$$

4n ni olish uchun 8n va -4n ni birlashtirish.

$$4m^{2}+4mn+8m+4n+n^{2}+4$$