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

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

Baholash

$$-4xy$$

Yechim qadamlari

Hisoblang: \left(x-y\right)\left(x+y\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

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

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

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

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

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

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

2y ga y-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2y^{2}-2xy+2y^{2}-2yx$$

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

$$-2xy-2yx$$

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

$$-4xy$$

Kengaytirish

$$-4xy$$

Yechim qadamlari

Hisoblang: \left(x-y\right)\left(x+y\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

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

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

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

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

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

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

2y ga y-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2y^{2}-2xy+2y^{2}-2yx$$

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

$$-2xy-2yx$$

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

$$-4xy$$