(x+2y)^2-(x+y)(3x-y)-5y^2 eching

$$( x + 2 y ) ^ { 2 } - ( x + y ) ( 3 x - y ) - 5 y ^ { 2 }$$

Baholash

$$2x\left(y-x\right)$$

Yechim qadamlari

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

$$x^{2}+4xy+4y^{2}-\left(x+y\right)\left(3x-y\right)-5y^{2}$$

x+y ga 3x-y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+4xy+4y^{2}-\left(3x^{2}+2xy-y^{2}\right)-5y^{2}$$

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

$$x^{2}+4xy+4y^{2}-3x^{2}-2xy+y^{2}-5y^{2}$$

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

$$-2x^{2}+4xy+4y^{2}-2xy+y^{2}-5y^{2}$$

2xy ni olish uchun 4xy va -2xy ni birlashtirish.

$$-2x^{2}+2xy+4y^{2}+y^{2}-5y^{2}$$

5y^{2} ni olish uchun 4y^{2} va y^{2} ni birlashtirish.

$$-2x^{2}+2xy+5y^{2}-5y^{2}$$

0 ni olish uchun 5y^{2} va -5y^{2} ni birlashtirish.

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

Kengaytirish

$$2xy-2x^{2}$$

Yechim qadamlari

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

$$x^{2}+4xy+4y^{2}-\left(x+y\right)\left(3x-y\right)-5y^{2}$$

x+y ga 3x-y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+4xy+4y^{2}-\left(3x^{2}+2xy-y^{2}\right)-5y^{2}$$

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

$$x^{2}+4xy+4y^{2}-3x^{2}-2xy+y^{2}-5y^{2}$$

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

$$-2x^{2}+4xy+4y^{2}-2xy+y^{2}-5y^{2}$$

2xy ni olish uchun 4xy va -2xy ni birlashtirish.

$$-2x^{2}+2xy+4y^{2}+y^{2}-5y^{2}$$

5y^{2} ni olish uchun 4y^{2} va y^{2} ni birlashtirish.

$$-2x^{2}+2xy+5y^{2}-5y^{2}$$

0 ni olish uchun 5y^{2} va -5y^{2} ni birlashtirish.

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