(x^{3}-y^{3}+3xy)^{2}-(x^{3}+y^3+3xy)^2+4xy^3(x^2+3y) eching

$$( x ^ { 3 } - y ^ { 3 } + 3 x y ) ^ { 2 } - ( x ^ { 3 } + y ^ { 3 } + 3 x y ) ^ { 2 } + 4 x y ^ { 3 } ( x ^ { 2 } + 3 y )$$

Baholash

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Yechim qadamlari

x^{3}-y^{3}+3xy kvadratini chiqarish.

$$x^{6}-2x^{3}y^{3}+9x^{2}y^{2}-6xy^{4}+y^{6}+6yx^{4}-\left(x^{3}+y^{3}+3xy\right)^{2}+4xy^{3}\left(x^{2}+3y\right)$$

x^{3}+y^{3}+3xy kvadratini chiqarish.

$$x^{6}-2x^{3}y^{3}+9x^{2}y^{2}-6xy^{4}+y^{6}+6yx^{4}-\left(x^{6}+2x^{3}y^{3}+9x^{2}y^{2}+6xy^{4}+y^{6}+6yx^{4}\right)+4xy^{3}\left(x^{2}+3y\right)$$

x^{6}+2x^{3}y^{3}+9x^{2}y^{2}+6xy^{4}+y^{6}+6yx^{4} teskarisini topish uchun har birining teskarisini toping.

$$x^{6}-2x^{3}y^{3}+9x^{2}y^{2}-6xy^{4}+y^{6}+6yx^{4}-x^{6}-2x^{3}y^{3}-9x^{2}y^{2}-6xy^{4}-y^{6}-6yx^{4}+4xy^{3}\left(x^{2}+3y\right)$$

0 ni olish uchun x^{6} va -x^{6} ni birlashtirish.

$$-2x^{3}y^{3}+9x^{2}y^{2}-6xy^{4}+y^{6}+6yx^{4}-2x^{3}y^{3}-9x^{2}y^{2}-6xy^{4}-y^{6}-6yx^{4}+4xy^{3}\left(x^{2}+3y\right)$$

-4x^{3}y^{3} ni olish uchun -2x^{3}y^{3} va -2x^{3}y^{3} ni birlashtirish.

$$-4x^{3}y^{3}+9x^{2}y^{2}-6xy^{4}+y^{6}+6yx^{4}-9x^{2}y^{2}-6xy^{4}-y^{6}-6yx^{4}+4xy^{3}\left(x^{2}+3y\right)$$

0 ni olish uchun 9x^{2}y^{2} va -9x^{2}y^{2} ni birlashtirish.

$$-4x^{3}y^{3}-6xy^{4}+y^{6}+6yx^{4}-6xy^{4}-y^{6}-6yx^{4}+4xy^{3}\left(x^{2}+3y\right)$$

-12xy^{4} ni olish uchun -6xy^{4} va -6xy^{4} ni birlashtirish.

$$-4x^{3}y^{3}-12xy^{4}+y^{6}+6yx^{4}-y^{6}-6yx^{4}+4xy^{3}\left(x^{2}+3y\right)$$

0 ni olish uchun y^{6} va -y^{6} ni birlashtirish.

$$-4x^{3}y^{3}-12xy^{4}+6yx^{4}-6yx^{4}+4xy^{3}\left(x^{2}+3y\right)$$

0 ni olish uchun 6yx^{4} va -6yx^{4} ni birlashtirish.

$$-4x^{3}y^{3}-12xy^{4}+4xy^{3}\left(x^{2}+3y\right)$$

4xy^{3} ga x^{2}+3y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-4x^{3}y^{3}-12xy^{4}+4y^{3}x^{3}+12xy^{4}$$

0 ni olish uchun -4x^{3}y^{3} va 4y^{3}x^{3} ni birlashtirish.

$$-12xy^{4}+12xy^{4}$$

0 ni olish uchun -12xy^{4} va 12xy^{4} ni birlashtirish.

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Omil

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