(1/2-a)^2-3(a-1/2)(a+1/2)+2(a-1)^2 eching

$$( \frac { 1 } { 2 } - a ) ^ { 2 } - 3 ( a - \frac { 1 } { 2 } ) ( a + \frac { 1 } { 2 } ) + 2 ( a - 1 ) ^ { 2 }$$

Baholash

$$3-5a$$

Yechim qadamlari

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(\frac{1}{2}-a\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}-a+a^{2}-3\left(a-\frac{1}{2}\right)\left(a+\frac{1}{2}\right)+2\left(a-1\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-1\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}-a+a^{2}-3\left(a-\frac{1}{2}\right)\left(a+\frac{1}{2}\right)+2\left(a^{2}-2a+1\right)$$

2 ga a^{2}-2a+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}-a+a^{2}-3\left(a-\frac{1}{2}\right)\left(a+\frac{1}{2}\right)+2a^{2}-4a+2$$

-3 ga a-\frac{1}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}-a+a^{2}+\left(-3a+\frac{3}{2}\right)\left(a+\frac{1}{2}\right)+2a^{2}-4a+2$$

-3a+\frac{3}{2} ga a+\frac{1}{2} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{1}{4}-a+a^{2}-3a^{2}+\frac{3}{4}+2a^{2}-4a+2$$

-2a^{2} ni olish uchun a^{2} va -3a^{2} ni birlashtirish.

$$\frac{1}{4}-a-2a^{2}+\frac{3}{4}+2a^{2}-4a+2$$

1 olish uchun \frac{1}{4} va \frac{3}{4}'ni qo'shing.

$$1-a-2a^{2}+2a^{2}-4a+2$$

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

$$1-a-4a+2$$

-5a ni olish uchun -a va -4a ni birlashtirish.

$$1-5a+2$$

3 olish uchun 1 va 2'ni qo'shing.

$$3-5a$$

Kengaytirish

$$3-5a$$

Yechim qadamlari

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(\frac{1}{2}-a\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}-a+a^{2}-3\left(a-\frac{1}{2}\right)\left(a+\frac{1}{2}\right)+2\left(a-1\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-1\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}-a+a^{2}-3\left(a-\frac{1}{2}\right)\left(a+\frac{1}{2}\right)+2\left(a^{2}-2a+1\right)$$

2 ga a^{2}-2a+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}-a+a^{2}-3\left(a-\frac{1}{2}\right)\left(a+\frac{1}{2}\right)+2a^{2}-4a+2$$

-3 ga a-\frac{1}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}-a+a^{2}+\left(-3a+\frac{3}{2}\right)\left(a+\frac{1}{2}\right)+2a^{2}-4a+2$$

-3a+\frac{3}{2} ga a+\frac{1}{2} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{1}{4}-a+a^{2}-3a^{2}+\frac{3}{4}+2a^{2}-4a+2$$

-2a^{2} ni olish uchun a^{2} va -3a^{2} ni birlashtirish.

$$\frac{1}{4}-a-2a^{2}+\frac{3}{4}+2a^{2}-4a+2$$

1 olish uchun \frac{1}{4} va \frac{3}{4}'ni qo'shing.

$$1-a-2a^{2}+2a^{2}-4a+2$$

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

$$1-a-4a+2$$

-5a ni olish uchun -a va -4a ni birlashtirish.

$$1-5a+2$$

3 olish uchun 1 va 2'ni qo'shing.

$$3-5a$$