4(x+y)^2-4(x+y)(x-y)+(x-y)^2 eching

$$4 ( x + y ) ^ { 2 } - 4 ( x + y ) ( x - y ) + ( x - y ) ^ { 2 }$$

Baholash

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

Yechim qadamlari

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

$$4\left(x^{2}+2xy+y^{2}\right)-4\left(x+y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

4 ga x^{2}+2xy+y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+8xy+4y^{2}-4\left(x+y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

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

$$4x^{2}+8xy+4y^{2}-4\left(x+y\right)\left(x-y\right)+x^{2}-2xy+y^{2}$$

-4 ga x+y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+8xy+4y^{2}+\left(-4x-4y\right)\left(x-y\right)+x^{2}-2xy+y^{2}$$

-4x-4y ga x-y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4x^{2}+8xy+4y^{2}-4x^{2}+4y^{2}+x^{2}-2xy+y^{2}$$

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

$$8xy+4y^{2}+4y^{2}+x^{2}-2xy+y^{2}$$

8y^{2} ni olish uchun 4y^{2} va 4y^{2} ni birlashtirish.

$$8xy+8y^{2}+x^{2}-2xy+y^{2}$$

6xy ni olish uchun 8xy va -2xy ni birlashtirish.

$$6xy+8y^{2}+x^{2}+y^{2}$$

9y^{2} ni olish uchun 8y^{2} va y^{2} ni birlashtirish.

$$6xy+9y^{2}+x^{2}$$

Kengaytirish

$$x^{2}+6xy+9y^{2}$$

Yechim qadamlari

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

$$4\left(x^{2}+2xy+y^{2}\right)-4\left(x+y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

4 ga x^{2}+2xy+y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+8xy+4y^{2}-4\left(x+y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

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

$$4x^{2}+8xy+4y^{2}-4\left(x+y\right)\left(x-y\right)+x^{2}-2xy+y^{2}$$

-4 ga x+y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+8xy+4y^{2}+\left(-4x-4y\right)\left(x-y\right)+x^{2}-2xy+y^{2}$$

-4x-4y ga x-y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4x^{2}+8xy+4y^{2}-4x^{2}+4y^{2}+x^{2}-2xy+y^{2}$$

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

$$8xy+4y^{2}+4y^{2}+x^{2}-2xy+y^{2}$$

8y^{2} ni olish uchun 4y^{2} va 4y^{2} ni birlashtirish.

$$8xy+8y^{2}+x^{2}-2xy+y^{2}$$

6xy ni olish uchun 8xy va -2xy ni birlashtirish.

$$6xy+8y^{2}+x^{2}+y^{2}$$

9y^{2} ni olish uchun 8y^{2} va y^{2} ni birlashtirish.

$$6xy+9y^{2}+x^{2}$$