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

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

Baholash

$$-2y^{4}$$

Yechim qadamlari

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

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

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

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

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

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

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

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

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

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

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

y^{2}x^{2}+y^{4} teskarisini topish uchun har birining teskarisini toping.

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

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

$$-y^{4}-y^{4}$$

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

$$-2y^{4}$$

Kengaytirish

$$-2y^{4}$$

Yechim qadamlari

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

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

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

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

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

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

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

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

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

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

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

y^{2}x^{2}+y^{4} teskarisini topish uchun har birining teskarisini toping.

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

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

$$-y^{4}-y^{4}$$

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

$$-2y^{4}$$