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x^{2}-xy+\frac{1}{4}y^{2}+\left(x+\frac{1}{2}y\right)^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-\frac{1}{2}y\right)^{2} kengaytirilishi uchun ishlating.
x^{2}-xy+\frac{1}{4}y^{2}+x^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+\frac{1}{2}y\right)^{2} kengaytirilishi uchun ishlating.
2x^{2}-xy+\frac{1}{4}y^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
2x^{2} ni olish uchun x^{2} va x^{2} ni birlashtirish.
2x^{2}+\frac{1}{4}y^{2}+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
0 ni olish uchun -xy va xy ni birlashtirish.
2x^{2}+\frac{1}{2}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
\frac{1}{2}y^{2} ni olish uchun \frac{1}{4}y^{2} va \frac{1}{4}y^{2} ni birlashtirish.
2x^{2}+\frac{1}{2}y^{2}+\left(2x-y\right)\left(x+\frac{1}{2}y\right)
2 ga x-\frac{1}{2}y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
2x^{2}+\frac{1}{2}y^{2}+2x^{2}-\frac{1}{2}y^{2}
2x-y ga x+\frac{1}{2}y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
4x^{2}+\frac{1}{2}y^{2}-\frac{1}{2}y^{2}
4x^{2} ni olish uchun 2x^{2} va 2x^{2} ni birlashtirish.
4x^{2}
0 ni olish uchun \frac{1}{2}y^{2} va -\frac{1}{2}y^{2} ni birlashtirish.
x^{2}-xy+\frac{1}{4}y^{2}+\left(x+\frac{1}{2}y\right)^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-\frac{1}{2}y\right)^{2} kengaytirilishi uchun ishlating.
x^{2}-xy+\frac{1}{4}y^{2}+x^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+\frac{1}{2}y\right)^{2} kengaytirilishi uchun ishlating.
2x^{2}-xy+\frac{1}{4}y^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
2x^{2} ni olish uchun x^{2} va x^{2} ni birlashtirish.
2x^{2}+\frac{1}{4}y^{2}+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
0 ni olish uchun -xy va xy ni birlashtirish.
2x^{2}+\frac{1}{2}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
\frac{1}{2}y^{2} ni olish uchun \frac{1}{4}y^{2} va \frac{1}{4}y^{2} ni birlashtirish.
2x^{2}+\frac{1}{2}y^{2}+\left(2x-y\right)\left(x+\frac{1}{2}y\right)
2 ga x-\frac{1}{2}y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
2x^{2}+\frac{1}{2}y^{2}+2x^{2}-\frac{1}{2}y^{2}
2x-y ga x+\frac{1}{2}y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
4x^{2}+\frac{1}{2}y^{2}-\frac{1}{2}y^{2}
4x^{2} ni olish uchun 2x^{2} va 2x^{2} ni birlashtirish.
4x^{2}
0 ni olish uchun \frac{1}{2}y^{2} va -\frac{1}{2}y^{2} ni birlashtirish.