(x-y+1/2)(x-y+1/2)-(x-y)^{2}+(1/3x^{2}-3/2)^3-x^2(frac{1}{27}x^4-frac{1}{2}x^2+frac{9}{4}) eching

$$( x - y + \frac { 1 } { 2 } ) ( x - y + \frac { 1 } { 2 } ) - ( x - y ) ^ { 2 } + ( \frac { 1 } { 3 } x ^ { 2 } - \frac { 3 } { 2 } ) ^ { 3 } - x ^ { 2 } ( \frac { 1 } { 27 } x ^ { 4 } - \frac { 1 } { 2 } x ^ { 2 } + \frac { 9 } { 4 } )$$

Baholash

$$x-y-\frac{25}{8}$$

Yechim qadamlari

\left(x-y+\frac{1}{2}\right)^{2} hosil qilish uchun x-y+\frac{1}{2} va x-y+\frac{1}{2} ni ko'paytirish.

$$\left(x-y+\frac{1}{2}\right)^{2}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

x-y+\frac{1}{2} kvadratini chiqarish.

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x^{2}-2xy+y^{2}\right)+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-x^{2}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$-2xy+x+y^{2}-y+\frac{1}{4}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x+y^{2}-y+\frac{1}{4}-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3} kengaytirilishi uchun ishlating.

$$x-y+\frac{1}{4}+\frac{1}{27}\left(x^{2}\right)^{3}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

-\frac{25}{8} olish uchun \frac{1}{4} dan \frac{27}{8} ni ayirish.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

x^{2} ga \frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\left(\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}\right)$$

\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2} teskarisini topish uchun har birining teskarisini toping.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{1}{27}x^{6}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

0 ni olish uchun \frac{1}{27}x^{6} va -\frac{1}{27}x^{6} ni birlashtirish.

$$x-y-\frac{25}{8}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

0 ni olish uchun -\frac{1}{2}x^{4} va \frac{1}{2}x^{4} ni birlashtirish.

$$x-y-\frac{25}{8}+\frac{9}{4}x^{2}-\frac{9}{4}x^{2}$$

0 ni olish uchun \frac{9}{4}x^{2} va -\frac{9}{4}x^{2} ni birlashtirish.

$$x-y-\frac{25}{8}$$

Kengaytirish

$$x-y-\frac{25}{8}$$

Yechim qadamlari

\left(x-y+\frac{1}{2}\right)^{2} hosil qilish uchun x-y+\frac{1}{2} va x-y+\frac{1}{2} ni ko'paytirish.

$$\left(x-y+\frac{1}{2}\right)^{2}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

x-y+\frac{1}{2} kvadratini chiqarish.

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x^{2}-2xy+y^{2}\right)+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-x^{2}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$-2xy+x+y^{2}-y+\frac{1}{4}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x+y^{2}-y+\frac{1}{4}-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3} kengaytirilishi uchun ishlating.

$$x-y+\frac{1}{4}+\frac{1}{27}\left(x^{2}\right)^{3}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

-\frac{25}{8} olish uchun \frac{1}{4} dan \frac{27}{8} ni ayirish.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

x^{2} ga \frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\left(\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}\right)$$

\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2} teskarisini topish uchun har birining teskarisini toping.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{1}{27}x^{6}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

0 ni olish uchun \frac{1}{27}x^{6} va -\frac{1}{27}x^{6} ni birlashtirish.

$$x-y-\frac{25}{8}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

0 ni olish uchun -\frac{1}{2}x^{4} va \frac{1}{2}x^{4} ni birlashtirish.

$$x-y-\frac{25}{8}+\frac{9}{4}x^{2}-\frac{9}{4}x^{2}$$

0 ni olish uchun \frac{9}{4}x^{2} va -\frac{9}{4}x^{2} ni birlashtirish.

$$x-y-\frac{25}{8}$$